When it comes time to move, a good toolkit is a must have. Whether you're taking measurements, hanging artwork, or assembling furniture, there are a few items you'll want to have on hand.
After I graduated college my dad put together a basic toolbox for me, which at the time I didn't think I'd have much use for. Little did I know how useful it would become as I bounced around from one apartment to the next. I've found that one of the most convenient aspects of a toolbox is having everything in one location, so that come time to take on a project I know exactly where to find (or at least look for) what I need. While there are many ways to beef up your toolbox, these 10 items are a great place to start:
• Tape Measure
• Hammer
• Screwdriver
• Level
• Box Cutter
• Stud Finder
• Pliers
• Cutting Pliers
• Saw
• Flashlight
Renting in the city, where space is limited, makes a compact and useful toolkit quite advantageous. One of the more highly used items I've added is an assortment of nails, screws, hooks and small accessories. Often these pieces are left over from purchasing in bulk and not needed again for some time. Throw the extras in your toolbox, so you're not repurchasing every time you move or need to hang something on the wall.

(Images: Lindsay Tella)

Howard Butcher Bloc...
Would also add a 5-in-1 tool to the list.
Someone gave me a toolbox with the items mentioned for a high school graduation gift, and I still use it, some 15 years later! I recently added a cordless drill, which is definitely worth the investment.
Ditto to everything @Bibliovore says, and definitely @Ecandle96 has it right with the drill. But if I could have only one drill, I'd choose corded over cordless because they're more powerful - many, many times a cordless drill won't have the power to predrill into a stud or whatever. If you're not using your drill/driver all the time, the inconvenience of having to plug it in is minimal, and you don't have to worry that maybe the battery's gone dead since you last used it six months ago. But if you do go with cordless, make sure it's at least 18v; and remove the battery when not in use.
You know what else - I'd add a pair of vise-grips. Definitely, vise-grips. They do come in a smaller size.
And keep a pair in the car, too. Along with a couple of scredrivers. Invaluable.
Good luck with the stud finder, if you have plaster walls -- as I found out the hard way =^p.
Otherwise, good list =^).
My favourite tool is a cordless electric screwdriver-drill that came with a bunch of attachments. The most frequently used is a 4 inch long Philips magnetic screwdriver tip, a gift from my son, who figured his mom (that would be me) just couldn't live without it. Smart boy!
RE: the spirit level... there's an app for that. Several actually!
Don't buy cheap tools; if you don't have the money to buy good quality ones. They won't last long and they won't do the job. You'll just waste money by later replacing them with quality tools. Only buy good quality brands. If you don't have the money right now you can find great prices for them at garage or estate sales or even ebay; if they are in good condition. As far as a drill goes, also be very careful about a cheap one. If you need to drill into plaster or brick you'll need one powerful enough to do the job. If drilling through drywall with no studs you may be able to use the cheap models. Never skimp on your tools. They can last forever if you make the right purchase. Again, if you're low on funds, check out the sales.
I got two of the Ikea Fixa toolkits a few months ago and I've used at least one tool from each kit every week since then:
http://www.ikea.com/us/en/catalog/products/00169254/
http://www.ikea.com/us/en/catalog/products/30169257/
The tools I use most are the multi-bit screwdriver, the tape measure, the level, and the hammer. One thing that seems minor that I've gotten a hell of a lot of use out of is the plastic cap that fits over the hammerhead so that the hammer can be used more like a rubber mallet.
I also have a Black & Decker corded electric drill (borrowed from my dad), but I'm going to give it back to him and get a corded hammer drill since one of my walls is brick and it is much better for masonry.
I also recommend having several sizes of clamps, especially if you do any DIY involving gluing. For bigger items, something like a one-handed band clamp (http://www.amazon.com/Wolfcraft-3681404-One-Hand-Ratcheting-Clamp/dp/B000JCLNQ4/ref=sr_1_4?ie=UTF8&qid=1346126531&sr=8-4&keywords=clamps+strap) can be a lifesaver.
If you're going to get an electric drill/driver (cordless or corded), look for one with a light. I don't have one but wish I did. My dad has one. Can't tell you how many times having a little spot light would have made the job easier.
This is a good list but some things I can't live without and use all the time are missing, but wow it's such a great spring board for discussion. I'm proud of my tool kit I've developed over the trial and error process of DIYing my brains out.
Here is my list!
http://shamelesslycheapdiydesign.com/2012/07/17/10-tooly-essentials-for-the-diy-dude-or-diva/