There is quite a few broad topics suggested for the LHC[1], and even right now there are 3 other experiments running on it[2]. (ATLAS is the Higg's boson experiment, although it isn't just looking for the Higg's boson.)

[1]: http://en.wikipedia.org/wiki/Large_Hadron_Collider#Purpose [2]: http://en.wikipedia.org/wiki/List_of_Large_Hadron_Collider_e...

Figure out how the heck the Higgs boson actually behaves, for starters (they just found it). But my understanding is the LHC is not a single-purpose tool. You can observe a variety of particles at a variety of energies.

edit: s/behave/observe/

They're going to shut it down towards the end of the year, refurbish it, and boost the energy level significantly.

http://press.web.cern.ch/press/PressReleases/Releases2012/PR...