My DD will be 2 in a couple of weeks. Here are the things she really loves to play with:
- funny hats (she has one with a duck head on it that she wears Every. Single. Day.) and socks (again, animal faces are a favorite)
- boxes that stack inside of each other (these are worth their weight in gold at our house)
- books of all kinds (though we have too many so I hope people don't get any for her birthday)
- wooden puzzles
- crayons, markers and drawing paper
I particularly want to second the PP's recommendation about containers. DD's most beloved toys at the moment are an empty pepper shaker, an empty oatmeal box, and a toy shopping cart in which she pushes them around. In general, anything that can hold other things is good.
Playsilks are also great, but if they're outside of your budget (they are for us), you can just go to a local thrift store and buy a handful of small scarves or handkerchiefs and put them in a special backpack, box, or basket. I have done this for birthdays and they just love it. Any sort of bright-colored fabric that is the right size for small hands to hold, fold, play with, drape, etc. is just fantastic for 2-year-olds. DD loves to play with my scarves, and my niece loves a tiny doll blanket that I made for her.
When my niece turned 2 a few months ago, I couldn't think of any toy she didn't already have (and didn't want to fill my brother's house with more stuff that he'd have to store). So I filled a small basket with little single-serving snacks that she loves: fruit snacks, granola bars, dried fruit, nuts, etc. That might be an option too.
ETA: I nearly forgot! DD also adores those "my first words" flash cards -- just simple ones with a picture on one side and the word on the other. She has a set with Sesame Street characters on them and can't get enough of them.