Dynamic rope Do not store your rope close to bleach, petroleum-based products, etc. Even the fumes can damage the rope.
Rope bag and/or tarp If you're flying, put the rope in a trash bag and close it tight to avoid exposure to harmful chemicals and fumes.
ATC device for belay and rappel
Helmet It's a must! Protects primarily from rocks and gear falling from above.
Chalk
Personal anchor system - PAS Some people use daisy chains, others - a couple of quick draws. I prefer either a Metolius PAS (http://www.rei.com/product/722384) or a BlueWater TLC (http://www.rei.com/product/782801).
Slings Long one or two for building sport anchors. A couple of shoulder-length for extending runners, attaching yourself to anchors, backing up rappel, etc.
Quick draws The exact number depends on the climb. Some sport climbs might require 20 or even more - consult your guide book.
Locking carabiners 5 for TR anchor, 1 for ATC and 1 for PAS (see below). But honestly, you can never have too many locking carabiners. :-)