Wooden Train set - My just turned 3 year old loves his
Cars/vehicles/trucks of various sizes, shapes and brands. We're now graduating to Matchbox/Hotwheels
B Parum Pum Pum Drum
Books
FisherPrice Laugh and Learn Home - He has played with this from 6 months on and continues to play with it. One of the best things I purchased. You can often find these used (I got my for $20 at Good Will)

Lego and more lego (ok, Duplo Lego). Cars, especially if their doors can open and they can be put apart (they will be put apart in any case). Wooden blocks of any kind. Kitchen toy equipment. Sturdy books, books about the alphabet and numbers are a big fav. Trains. Puzzles... especially with cars and trains :-). For older toddlers: magnets (big magnets one cannot ingest).
>>> I have a 2 and half years old son, which, of course, preferes age inappropriate toys and does not particular care for teddy bears or dolls but sometime will cuddle one of the many he has received.

Bristle Blocks and beach balls.

Best toy we have EVER bought: Imaginarium Marble Race. You can get it at Toys T Us, online, it's only $20 but EVERYONE loves it. We got it when my older son turned 3 (the marbles are a choking hazard), but my 2 yr old son loves it, too. I once gave this as a gift to my nieces, who really enjoy it, but it ended up being played with mostly by their dad, his brother and grandpa! Girls usually love it, too. I admit it's also my favorite toy around here as well. ;-)

My 3 year old twins can't get enough of magna tiles. They started playing with them at 2.5. I can't say enough great things about them!

http://www.magnatiles.com/

I wanted one of these so bad as a little girl. I'm really tempted to get it for my daughter so I can play with it. This and a remote control car were things I asked for year after year, but never received.

play kitchen!

I love all the recommendations so far. One more: turn something into a ball pit! Buy a big bag of ball-pit balls (there are some that are non-PVC, phthalate-free, etc., though they cost more), and toss them in a pack-n-play or a small pop-up play tent. There's the storage issue, but you don't need very many for a toddler.

Well that all depends. Do you like the parents, or maybe you are said parent? Maybe some of those nifty invisible markers stuff they make now so no one has to clean up the inevitable carpet or wall art.

Do you not like the parents? These should do it.

The B's are always favorites:
Balls
Blocks
Books
Babies

Also: crayons/big pad of paper, stickers, play food, anything that allows them to be a grown up (my daughter loves her broom/dustpan and small snow shovel).

A water/sand wheel. Great for the bathtub, sink, sandbox, kiddy pool, and water/sand table. It actually teaches pre-math concepts of size, volume, and gravity.

http://www.fisher-price.com/en_US/product/56981

The Fisher-Price cash register. All three of my kids spent countless hours playing grocery store and every other store they imagined...

Dress up outfits (doctor, fireman, vet, etc), play food, play kitchen, any book by Mo Willemstad, especially his new one Goldilocks and the Three Dinosaurs.

Mo Willems. Darn you autocorrect.

Cardboard box!! Seriously, they'll play for hours in one! :o)
I'm not one to avocate sticking your child in front of a TV but there are some really nice DVS's/Blue Rays out that that are not only entertaining but have lessons and it's never too early to learn good manners! .

Doctor's set :-)
All made of wood and my son has been playing with it for about a year now. He is two and a half. It is so sweet how he treats me, daddy, grandpa or also his doll by giving us "pills" and shots and he even pretends he is writing a prescription on a cute little book that is part of the set!

A bead stringing set that includes alphabet shapes. Too big to be swallowed, easy enough to stow away. Teaches both letters and hand eye coordination.
Puzzles, balls, and blocks are also great.

It depends whether you are trying to please the kid or the parents. Nothing that makes noises if you are concern with the parents. Children hate getting clothes as gifts, they also hate gifts that needs to be shared.

I often go with picture books, sports items, cute custom stamps with their names so that they can "mark the territory"... There are things that children don't hate and please the parents. (I don't have kids myself, I'm more concern with pleasing the parents.)

A good set of blocks will be enjoyed well past toddlerhood! Ditto other open-ended play items, like scarves, dress-up items (some of the best ones are castoffs from your closet), Play-Doh...

handmade plushies!

http://stellaandmaude.com/

duplo, green toys big truck, school bus etc, soft dolls (PBK baby are a big hit here), play kitchen, playsilks, balls, large boxes

Rody, a grocery cart, and a doll stroller all get huge play at out huse and at toddler playdates. Harmonicas too and kazoos

Wooden blocks, pop-up books, stacking cups (good for water, sand, or kitchen play), anything with wheels. I have a one-year-old.

Duplos (especially with animals), trains, doll stroller, and shopping cart have been big hits among the toddlers in our circle.

and these
http://www.rodytoy.com

http://www.wheelybug.com
(the small is great for my 2 yo, got it when she was 1 and still fits well).

Stomp rockets. The toddler size. Ok for small indoor spaces

Easel, paint, different size real brushes, roll of paper. Wooden puzzles. Play kitchen. Costume bin. Refrigerator box!

Oh yes! A wheely bug! And Wheely Moo. (We had one in each size in our house -- they still love zipping around on them at ages 6 and 9)

I'd suggest open-ended stuff -- especially costumes. The most-used item when my kids were little (they each used it in turn) was an elephant costume I picked up on Halloween one year for $7. They each wore it for Halloween for a couple of years, and play with it all the time (even if it is a bit small).

These are another favourite source:

http://www.dreampowercostumes.com/

Also, some costumes from the Disney Store (a Pirate), and bits and pieces picked up in odd places. An astronaut's helmet, police cap, cowboy hat, angel wings, doctor's scrubs and coat (and yes! a doctor's kit!!)... These keep them occupied for hours.

Being Canadian, I think all costumes should be stored in a Tickle Trunk like Mr. Dressup's. It would be a fun idea to buy a foot locker or steamer trunk, or a simple plain wooden trunk, and either paint it or cover it with wonderful stickers...

As for stuffies, my kids still love their Jellycat Bunglie Bunny and ZidZid Kid stuffed animals and dolls.

http://www.zacandzoe.com/misc/zzcushions.html

My son still loves his Dylan Freeth wooden vehicles from Habitat --

http://www.habitat.co.uk/london-bus-kid's-wooden-toy/toys//fcp-product/27403

As for books, besides Mo Willems (! much beloved in our house), there are books by Eric Carle, Sandra Boynton, Dr. Suess... They've loved I Want My Hat Back; Where the Wild Things Are; Make Way for Ducklings; Blueberries for Sal; Chikka Chikka Boom Boom; Sheep in a Jeep (Sheep Out To Eat; Ship on a Ship; Sheep in a Shop; Sheep Trick Or Treat); Goodnight Gorilla; I Am A Bunny, and all the Robert Munch books... just so many wonderful books!

Buying presents for kids is so much fun!

A cardboard Appliance box, a box of crayons or makers, and YOUR TIME to create a castle or a rocketship or fillintheblank

My son loves to draw and I bought him a crayon roll from etsy. I love that it's handmade and that it keeps the crayons organized. We never leave home without it! I actually just bought 6 more for all my nieces and friends' children; it's my to-go gift for toddlers. Lots of drawing envisioned for the holidays!

http://www.etsy.com/shop/elikan?ref=search_shop_redirect

My kids are 11, 9, 4 & 10 mos. These are tried & true for all of my kids over the yrs.:

Lego anything

This drill "game":
http://www.amazon.com/Educational-Insights-Design-Activity-Center/dp/B00012O42W/ref=sr_1_1?s=toys-and-games&ie=UTF8&qid=1354847342&sr=1-1&keywords=drill+set+for+kids

This cash register:
http://www.amazon.com/Learning-Resources-Teaching-Cash-Register/dp/B0006N8X3M

Books. I especially recommend Robert McCloskey's Make Way for Ducklings and Blueberries for Sal, all the Dr. Seuss books, Where the Wild Things Are, Goodnight Moon, the Frog and Toad books, Peter Rabbit.

Magformers and Magneatos are two favorites in our house!!!

Lyonstill and urbancricket have already said a big cardboard box, and they are right! Also just about anything real: gardening, painting, cooking. I have a pretty dim opinion of 'toys'.

Any kind of indoor action toys to help kids spend their energy during the cold winter months. We are getting our twin 2yo boys a bouncy trampoline, a basketball net set, wheelie moos, and lots of cars and art supplies.

Books on CD for the car. It's a winner at any age.

Dots! Super cheap and super fun!

http://www.dotart.com/

@Freeamy73: yes on the car books! Especially if holiday travel involves a long drive! If you're feeling flush, add a kiddie MP3 player and put some of those stories on it:
http://www.amazon.com/SweetPea3-MP3-Player-Kids-Blue/dp/B001M1L44W/ref=sr_1_1?ie=UTF8&qid=1354883775&sr=8-1&keywords=sweet+pea+mp3

A toy vacuum cleaner. Or better yet, a real vacuum cleaner in miniature.

Toddlers are easy to please. Mine loved coloring on cardboard boxes, "going to the store" with her tiny shopping cart, using the magnadoodle/aqua doodle, painting on her easel, lining up her Little People, using stacking boxes, doing animal shape puzzles... Jeez and if I ran out if stuff to do I gave her a bowl of dried beans and a few boxes to pour them into... Heehee... :)

Toddlers are easy to please. Mine loved coloring on cardboard boxes, "going to the store" with her tiny shopping cart, using the magnadoodle/aqua doodle, painting on her easel, lining up her Little People, using stacking boxes, doing animal shape puzzles... Jeez and if I ran out if stuff to do I gave her a bowl of dried beans and a few boxes to pour them into... Heehee... :)

homemade playdough: http://mommyfootprint.com/the-perfect-home-made-play-dough-recipe/

lift-the-flap books

play kitchen

duplo

plastic animals (e.g. Schleich)

I don't have any suggestions, but what do you get a toddler that has his own iPad?

Those nifty invisible markers are on our Christmas list for our two and a half year old. The only downside is that the coloring books that the markers work on are kinda pricey ($4.99 for a pretty small amount of pages). BUT, for some reason my daughter has colored the same pages over and over again on the two we bought, and one of them was the one that included the markers, so it's worth it for us! I think it probably helps that she can use them without us having to say no too much. I mean, when you're two you pretty much hear that word WAY too much in your little life.

And I can't stress how good of a gift books are. YOU CANNOT GO WRONG.