Time at the LHC
there will definitely be supersymmetrywhich isn't really a prediction at all, since it doesn't specify measurable parameters which have meaning for experimentalists. According to Woit, the predictions of Veltman include no fairy field and the realisation that string theory is mumbo jumbo.
Can we do any better? Tony Smith's composite Higgs is a possibility, but many approaches would lay claim to it. Is there something distinctive that might arise from a more Galoisian gravity? What truly new $p = 5$ process might we observe? The first possible experiment along these lines that came to my mind has nothing to do with the LHC. The difficulty is in imagining a material that could create a field quite unlike the usual suspects. A high temperature ceramic superconductor is one possibility. Having eliminated magnetic fields, one could look for Stern-Gerlach type pentuplet splittings of monoenergetic electron (or muon) beams.
I predict that the surprises (besides a lack of fairy field and sparticles) will mostly come in the analysis of multijet processes, where QCD predictions fail spectacularly. If I wasn't such a scatter brain, I would still be working on operad combinatorics for QCD.