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.
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.