We have lived together for almost 5 years now and have lived in 2 apartments and 2 houses, so we didn't really need too many "typical" things. I mainly registered for "upgraded" versions of stuff we already have (new pots/pans, new plates, new towels) and for cool stuff like vases, candles, etc.
What I'm most excited to get is my bedding. We just got our new bedroom furniture delivered 2 days ago and I've never splurged and bought really nice sheets, pillows, etc, so I really hope I get that stuff.
We registered at Bed Bath & Beyond and Target (even though I'm a little worried about Target because I've heard some negative reviews).