If we find no Higgs boson right now, there's still other options: multiple Higgs bosons, composite Higgs bosons, etc. We're only looking for the most simple configuration right now. If does do not exists (and it will take many many years to prove that), we're having a bit of a problem as this invalidates the central tenet of quantum field theory.

All of quantum field theory is based on the principle of local gauge symmetry. This means that by demanding the field be invariant under the transformations of a certain mathematical framework, the interactions appear automatically (don't worry if you don't understand that, that would take more than one HN post). This is all very beautiful but the problem is that this only works for massless fields. The Higgs mechanism solves this by instead of postulating mass as an intrinsic property of a field, it supplies mass as an extrinsic property.

Technically speaking all fields are still massless, yet due to their interaction with the Higgs field, they behave as if they had mass! This is good, because we can keep our precious gauge symmetries and particles can have mass which is a very basic experimental fact. (I'm ignoring some important parts here, like symmetry breaking, but this post is already getting too long).

If no Higgs is found, either some brilliant mind must find another solution to preserve the principle of local gauge symmetries, or we must leave field theories behind and look for another solution.

I personally hope no Higgs is found, as Higgsless theories look more appealing to me. Obviously, Nature shouldn't conform to my personal aesthetic views, so if proof for Higgs is found, I will have to accept that.

More or less the happy sense of being proved right. Since the Higgs is well-modeled and well-understood in theory, other than the value of its mass, we already have a rudimentary scientific understanding of what it does and how it works. But it's critically important that these theories, like the Standard Model that predicts the Higgs, be experimentally confirmed--though you are right that it would be far more earthshaking if it didn't appear.

It's just a model - finding higgs will add validity to that model as a useful tool. not finding it - invalidating that theory puts us back to the drawing board and/or focuses people on other theories. It's not the end or beginning of anything, just another step.

I want my time travel and anti-gravity and FTL drive, at consumer prices. I want to see dinosaurs and travel around the universe in the blink of an eye. Keep working science people.