For appliances, I recommend a KitchenAid Stand Mixer if you like to cook or bake; the Cuisinart combination food processor/blender; a Rival crockpot (great for having dinner ready when you get home, and also for keeping food warm for buffet dinners/parties); an iced tea maker; an electric knife (a lifesaver on Thanksgiving); a good coffee maker. We also love our George Foreman grill, but I'd try to get a new one with the removable grids that will go in the dishwasher.
For serving pieces, I like crystal or glass b/c they will always match even if you get new dishes, paint the kitchen, move etc. Some of the pieces I love that I use all the time are a chip and dip set (use that practically any time we have company, no matter how casual), a cake dome (I often leave it on the counter with whatever I have baked that week), and a trifle bowl (throw just about anything in this -- fruit, salad, pudding layered with cool whip -- and it looks fancy). I also love my big wooden salad bowl.
A good set of stainless steel mixing bowls, stainless steel measuring cups and spoons will last forever.
Corningware is great for casserole dishes.
A set of Pyrex with lids -- good for baking casseroles, pies, etc.
Two good cookie sheets.
A good set of pots and pans.
Bathroom accessories, such as toothbrush holder, etc.
I really like Pfaltzgraff for everyday dishes. They are wonderful quality, dishwasher safe, and have a ton of cute patterns. Check out their website.
A set of everyday flatware -- Oneida or Pfaltzgraff are good.
We registered for good china (Royal Doulton) and good crystal too. I am so glad I did b/c I really enjoy using them now that we have a dining room. I wish I had also registered for a good set of flatware -- I ended up buying it years later (Lenox).
Everything you need for bedding is also good -- comforter, dust ruffle, sheets, mattress pad, pillows, pillow protectors.
A good vaccuum cleaner, plus a dustbuster or something similar.
Cloth napkins, placemats, and napkin rings. Tablecloths if you know the size of your table.
Any electronics such as an alarm clock, phone, DVD player.
I really like Bed Bath and Beyond, several of my friends have registered there and I always get 20% coupons in the mail for them.