My children are now at secondary school so I'm not up to date with the latest toys. I know for my sons first birthday I bought him a little kitchen which had a shape sorter and pop up toast which made a funny noise and a few other activities on it. I'd have a look at the Early Learning Centre catalogue and have a look in Toys R Us to get some ideas. Shape sorters are usually good, as are plastic beakers which can be stacked or sorted into each other. The ones we had had some which had holes in so they could be used in the bath/sand pit aswell. The thing with a 1 year old is that they don't expect much so you don't have to go mad with toys. A bit of crinkly wrapping paper and a cardboard box they can sit in is usually as much fun as anything else!
Btw I remember for my sons first birthday and Christmas, which are quite close together, I put some toys he was given away and got a new one out every few weeks - he really enjoyed playing with the new toys.
I've just bought a baby walker for a friend's year-old baby. It has bricks and shapes in it, as well as several other activities, plus a hooter, a mirror, etc. I chose this, because it's educational, fun - and will steady baby when she finds her legs.