Bath toys are a good idea. My standard gift for 1-year-olds is a little set of three rubber duckies, and a mama duck (who is, inexplicably, also yellow). Very popular.
As is the popper. I kid you not, my 5-year-old son was zooming that thing around the back porch just last night.
something with a snake. he is a snake child. perhaps a cool stuffed/plush toy snake?
great suggestion reprise. fun for the whole family!
One year olds don’t generally need a lot of stuff (although I like the shoe idea). Whatever you get is really for the parents – they’re the ones who are going to appreciate it, and thank you for it.
Get mom a visit to a spa (or a Harry Potter broom ;)), get dad a subscription to Playboy (or Car & Driver).
Thanks for the suggestions so far 
I’m leaning towards a book or the broom 
( ->Reprise you evil girl) at the moment.
If you’re only 1, then you probably don’t have a lot of money to spend on a gift. After all, it’ll be a long time before you reach your prime earning years. So inexpensive is definitely the watchword here. I’d just toddle over to Pic ‘N’ Save and see what they’ve got.
<<<rimshot>>>
According to the woman I accosted at Toys R Us earlier this year, one year olds like to put things in other things and then take them back out.
Using that knowledge, I’ve bought a few baby gift this year, and the parents all claim that their kids like playing with the toys. In fact, I’ve actually seen them and they seem to enjoy themselves.
Playskool makes a nice line of toys that are relatively cheap and are labelled with appropriate ages.
I’ve four nieces and nephews, and while later years deserve deeper consideration, at one they’ve always been max happy with a stuffed critter (artificial, of course).