You'll want a way to carry water, whether in a water-bottle mounted on the bike (bottle mounts are cheap) or in a Camelback (more costly).
The above is about all I'd put under the category of "need". But you could also think about
:
* Spare tube and some tire levers, in case you get a flat while riding.
* Small pump that you can carry along, in case of a flat.
* Gloves -- I like to wear gloves when I ride.
* Multitool in case you need to adjust something on a ride.
For some of us, the list goes on infinitely.