I could go on and on and on. My daughter just turned one a few months ago (okay, 6 months ago, but it feels like yesterday!), and here are a few things we love:
1) Books - not an "exciting" gift, yes. Never ending fun for the birthday girl? YES! Just be sure to avoid the pop-ups. Oh gosh. Those rip out easily!
2) Inexpensive ride ones - this one is our favorite: http://www.littletikes.com/toys/push-ride-doll-walker.aspx
3) If you have more money to spend, try this V-tech - http://www.littletikes.com/toys/push-ride-doll-walker.aspx - My daugter LOVES this thing! It's never ending fun. Serious fun.
4) Little Tikes Doll House: Old Skool toy like http://cgi.ebay.com/Little-Tikes-Pink-Roof-Grandmas-House-Dollhouse-More_W0QQitemZ110359795344QQcmdZViewItemQQptZLH_DefaultDomain_0?hash=item110359795344&_trksid=p3286.c0.m14&_trkparms=72%3A1205%7C66%3A2%7C65%3A12%7C39%3A1%7C240%3A1318%7C301%3A0%7C293%3A1%7C294%3A50- it's amazingly fun, especially as she grows older. I'm sure you could find a cheaper one, but this is just the first one I found.
5) Building blocks - nothing is more exciting than building things. We made our own, but there are plenty you can buy too.
I'll try to think of more - my own kids are screaming for attention. Literally! My 5-minute break is up!