Hmmm. The twins aren't 1 yet, and they weren't our first kids, but a few notes.
They started fighting over toys at 5 mos. So, having two of anything is a good idea rather early on. (That said, two doesn't always help -- the toy in a brother's hand is clearly the best toy in the house...)
Favorite gift so far? Probably the baby blankets knitted by a neighbor. Gorgeous and thick, and both blue, but subtly different shades. We're just getting to the point where fun gifts make sense (as opposed to functional things like clothes).
Oh, and on clothes... if you're buying clothing gifts for twins, it'd be worth asking (or noting) the way they're being dressed. For instance, we dress the two boys in different colors on purpose, so we can tell them apart easily. We've gotten a number of gifts of matching (identical) clothing items. (What ends up happening is that only one twin will wear that item... they can just wear it twice the same week!)
mommy to three boys: A, 3/04
and identical twins B and D, arrived 9/08