A battery operated drill w/bits. Make sure it has bits for screws.
A glue gun
A good staple gun and lots of staples handy
If you sew, a descent sewing maching with plenty of thread and bobbies.
GOOD paint brushes and paint supplies
A good hammer
A line level
Spackle and spackle tool. (sorry, don't know the true term).
A decent ladder
Patience and good friends. :o)

I'd add to the previous lists masking tape, paint stripper, sand paper, and a selection of spray paints. Oh, and a few spare tarps.

scissors and more scissors. at your desk, in the kitchen

I do a ton of different crafts... I think I use hot glue, freezer paper, cardboard, acrylic paints, felt, pinking shears, scissors and sand paper the most. oh also wood glue :) if you wanted more, I would say a square for straight lines

Honestly, I buy my supplies on demand. That way I have the right tool for the job and I'm not trying to make do with something makeshift. I find when I buy things "just in case I need to..." I end up with a lot of junk.

That being said, get supplies based on the kind of projects you'd like to DIY. If you're working with fabrics for pillows and curtains, a sewing machine is obviously a good choice. If you're going to be refinishing furniture or building your own, a cordless drill, small sander and a decent hammer are all good tools to have. Straight edges/rulers, cutting tools (scissors, box cutter, xacto, etc), and a work surface are great for almost any project.

Good question but agree kinda depends on the crafts, I don't do any real woodwork, so...

hot glue gun/glue sticks
scissors
printer
sewing machine
acrylic paints/brushes
measuring tape/yard stick/ruler
clamps
pencils
iron
hammer/nails

I'd add:

A paper cutter
Glue Sticks
Stapler
Images from magazines and cards
Random bits of card stock and paper

You can do an amazing amount of crafts with very few supplies.

Stuff I use in just about every home improvement project: spider anchors, cordless drill with bits (esp. useful are the countersink and masonry drill bits), staple guns, clamps, and a hammer.

Hot glue gun/glue gun sticks
large ruler
exacto knife
measuring tape
sewing machine with all the thread imaginable
fabric
painters tape
electrical tape
foam core

I could keep going since 10 is limiting!

SPRAY ADHESIVE! It's good for a whole ton of stuff, and even works on fabric.

Good scissors for fabric and paper. (Separate ones!)
Good quality papers, pens, markers, etc.
Measuring tape, ruler.
Xacto knife and cutting mat.
Sewing machine. Doesn't have to be fancy, just get the job done.
Various colors of threads like black, white, gray and a few other colors.
Basic tool kit with hammer, screwdrivers and misc. nails and screws.
Variety of paints and good brushes.
Craft glues. One basic and one stronger glue for ceramics, etc.
Safety glasses.

Camera to document everything!

I'm not super crazy about hot glue myself. I prefer to have Household Goop or E-6000 on hand. Either holds just about anything forever.

It is good to have a toolbox and decent tools. A decent cordless drill is a must. For bits, I like to have a driver bit with a sleeve (and accompanying phillips bits in #1, 2, and 3) along with a good set of drill bits. (I have a regular set and a masonry set. The masonry set is great for things like drilling holes in plant pots and a must for drilling into tile) Among the other things to keep stocked: screws (I mostly use size 6 and 8, and typically the 3/4" to 1 1/2" range), finishing nails (handy for many things), a screwdriver (I like the kind that have both size 1 & 2 Phillips and flat in one tool), an adjustable wrench (a small one is fine), pliers, needle nose pliers, hammer, level, tape measure (I like one with both metric and imperial-just in case), a couple of flexible vice grips, a couple of good paintbrushes, painters tape, a five-in-one tool, lightweight spackle, a spackle knife, safety glasses.

On the more crafty side, if you ever want to do anything with fabric, a sewing machine (a vintage Singer from Craigslist is the way to go), fabric scissors, straight pins, thread and spare bobbins. A good set of exacto knives andd a mat or utility knife are good basics to have.

If you have the space, a circular saw is super handy (and doesn't take up much room) to have.

Pliers!
Pliers!
Especially if you are a chainmailler LOL
Thanks for the list!

Pretty much depends on what kinds of crafts you do! The other commenters pretty much covered all the things I thought of mentioning. :)

I mostly do very low-key framing/photo-type projects and always wish I had the space for a paper cutter. I also find I need photo-mounting squares a lot more often than I'd expect. There are lots of other very small things I never think to buy until I desperately need it. i.e. pencil sharpener, ruler

All great ideas. Did anyone say MODGE Frakkin PODGE???

above all things a paper cutter, good scissors (one for fabric, one for paper, off limits to silly husbands who use the paper scissors to cut off stuck shoe laces...) and a modge podge equivalent (frankly, the fancier version is so much better and I feel like it makes my decoupage projects look more grown up- you can choose the finish and... it is just way better. Golden makes something called soft gel which is my favorite).

Focused on paper crafting but drifts towards 'household projects' and

- blank cardstock in various sizes / colors; vellum is also nice to have on hand
- blank stickers in various sizes / formats (these few things I buy on sale/clearance and store in a small file box)
- good cutting tools, including a self healing mat and triangle or t-square in addition to a metal ruler, small Olfa break-off knife (handier and safer than Xacto) and a pair of scissors reserved for fabric & ribbon ONLY.
- a 'bone folder' if you work with paper a lot
- velcro!
- wood glue
- lightweight drill/driver (pilot holes are a crafty girls best friend), hand tools, I recommend small vice-grips and needle nose pliers for taking things apart. A rubber mallet is good to have too.
- unbleached white cotton string/yarn. I have a big spool of it and its so versatile- I've crocheted with it, trussed chickens with it, tourniquet-clamped chair legs with it, wrapped gifts with it, etc
- ribbon, there's never been a roll of ribbon I've regretted buying.
- markers, need not be fancy. I don't use them lots but when I do I'm very glad I have a box of Mr Sketch!

and.... ? and sewing. :)

Mod Podge!!! It comes in a hard coat, clear coat, matted coat ect. Its great of 3-D letters to giving an old wire planter a shine to the new paint as you turn it into a bed crown. I tried to decoupage some comic book pages on to the front of a dresser without it and the other stuff I used failed. Its easy to clean up its easy to use and its easy to take off if you mess up. It may not be the main component in your projects but for alot of them its a good finishing touch.

How funny, I was literally listing this exact thing out today. My top ten most universally helpful tools are:
1. tape measure
2. hammer
3. electric drill - with bits and screw heads
4. a variety of sizes and styles of screws (you will collect these over time anyway)
5. tack nails, when a screw just won't do
6. laser line level
7. stud finder
8. hot glue gun and sticks
9. heavy duty staple gun and staples
10. scissors, paper and fabric.

And whoever put a ladder on their list, bravo. good one. Also for the more hard core, power saw, sewing machine, and painting supplies most of which you can clean and recycle.

Great lists so far! I'll add:
1. handsaw - Stanley "Sharptooth" are excellent & can generally be found for less than $10.
2. foam rollers
3. metal T square (My wooden rulers & yardsticks always get broken anyway)
4. handheld vacuum for keeping sawdust & other little messes cleaned up
5. seam ripper
6. liquid nails or another construction adhesive
7. a clamp-on shop lamp for light exactly where you need it + extension cord
8. old hand towels & tee shirts cut up for shop towels
9. old sheets for drop cloths
10. organized storage - Not being able find what you need when you need it really stinks!

I think Centsational Girl did a post on this a couple of months ago... lemme see if I can find it...

Here we go! http://www.centsationalgirl.com/2011/11/my-25-essential-diy-tools/
It's 25, though, not 10, and they're pretty much all carpentry tools. I would add a decent sewing machine and iron/board.

I'm a quilter, so my list is pretty focused, but I might as well throw it in here:

1. a pair of excellent use-only-for-fabric scissors. Hide them, if you must, to make sure no one uses them to cut paper
2. seam ripper
3. butcher paper for applique
4. sharp, extra fine pins
5. a fairly heavy iron that makes lots of steam
6. iron on double sided fusible
7. iron on stabilizer
8. 65 mm rotary cutter with extra blades
9. selection of rulers
10. A tool box (a bait box I have repurposed) to keep all my supplies in one place SO I CAN FIND THEM.

Most of these have already been mentioned, but I'll echo them:
- Hammer
- Battery powered screwdriver/drill
- Levels (a small one for hanging art and a larger one for small renovation projects)
- A decent sewing machine with lots of white, off-white and black thread
- Drywall plaster for patching holes, a small can of primer and small cans of paint to match your walls (I keep small containers of each of my wall paint colors so they are easy to access for touch-ups) - and keep a couple of clean, good quality paint brushes on hand as well.
- Good quality scissors (I keep a pair for crafting, a pair for fabric and a pair for gardening)
- A glue gun and crazy glue
- A tape measure (I also keep a little one in my purse)
- A rotary cutter and mat (especially for sewing projects)

I'm calling this out as a web-traffic-boosting gimmick -- unless there really is someone out there who thinks "I ought to get strangers to tell me things to buy that I can't live without even though I've never needed them so far."

If it really is a sincere request for a shopping list of "things that will come in handy someday," I suggest the following:

--Three-hole punch
--Pinking shears
--Build-it-yourself casket hardware
--Moss-covered three-handled family gradunza
--Rickrack assortment
--Clock parts
--Bessemer converter
--Solar-powered glue gun
--Cornstarch
--Shoe trees

Some platitudes that are musts when you plan to purchase.

Do you have everything you need to measure twice, cut once?
Do you have a safe space to work in? Secure, firm, big enough.
Do you have everything you need to unstick what you stuck?
Do you have precision tools to ensure precision work, and make sure you don't injure yourself?

Generally, gorilla glue, acetone, stitch witchery, clamps, tarp, spray starch, iron, hammer, mallet, wood glue, alcohol, screwdriver with changeable tips, cordless drill. It's better to plan a project carefully, make lists, then get what you need. Until you've done about 10 projects, it's unlikely you will always have what you need to do a spur of the moment project. If you do buy specialty equipment, read the manuals, and make sure to get accessories for specific tasks.

Not enough mention of large and small phillips head and flat head screwdrivers.

But there aren't merely 10 items. So accumulate as you find the need, but don't get RID of any tools! (Consumable supplies should be kept until unusable or consumed.)

Respirator with filters rated for solvents & fine dust ($25-30 - your lungs are worth it....)
Golden Acrylic Gel Medium (for paper mache)
Gesso
Cheap brushes you can toss (Ikea!)
PC 11 epoxy
Carpenter's glue
Right angle square
Tweezers
Tinsnips
9 gauge hardware cloth
Roll of aluminum flashing
Leather work gloves that fit

For sewists: good shears, good thread snips, and good embroidery (small scissors), a steam iron and ironing board, mutiple fabric tape measures, a sewing gauge with 1/4, 3/8, 1/2 and 5/8 inch marked off, a range of sewing machine needles, paper scissors, wash off markers, soap slivers (for marking dark fabric), magnetic pin holder, glass headed pins (you can iron over them), and fusible web. A rotary cutter and mat are good as well.

General: dedicated paper scissors, hole punch, spray adhesive, Elmer's glue, fabric glue, hot glue gun, metal ruler, yard stick, clips, craft paper, and parchment like paper to trace upon.

I keep
~colorful magazines
~ Charms, Feathers, String/yarn (colored)
~ Puzzle glue (it drys clear!)
~ Clear Packing Tape
~Glass - Tile - Sand
~glass cutter
~paint- glossy
~acetone
~zippers (lots of them! you can put a zipper on anythign pretty much!)

Everyone suggesting Mod Podge, I HIGHLY recommend you try Royal Coat. Do you ever find your decoupage projects stay a little tacky unless you use a sealer over the top? Royal Coat has a built in sealer but otherwise it is basically the same thing. It's great.

@ BeeforBrian

If you took a second to read the question, which by all intents and purposes was a "GOOD" question or else it wouldn't have been accepted by Apartment Therapy in the first place, you would have noticed that the person asking the question asked those who already DIY to provide a list that THEY can't live without, not the person who is just starting out.

thanks for your useless list of whatever-the-heck-they-ares.