Contests
Besides Field Day there are other operating contests covering all the bands, from HF to UHF, and all the modes available to ham radio operators. You don't have to compete in the contest to participate. Just being around seasoned hams, observing how they operate and trying out new modes of operating is worth it. And perhaps you will get some new DX contacts, which count toward one of the many DX/operating awards that are available.
For more information, check-out the ARRL Contest Calendar at
http://www.arrl.org/contest-calendar
About two-thirds down the ARRL "contest-calendar" webpage is the "Contest Corral", which lists both ARRL and non-ARRL contests. Click on the month you are interested in to open a pdf that lists contests from all over the world. The "Contest Corral" is also published each month in the ARRL magazine QST. QST is a valuable source for information about what's going on in the world of ham radio.