For plenty of us, AndrewKemendo is right... learning that there is life on Mars would not answer any particularly fundamental questions. Maybe because a lot of people simply take it as a given that life exists on other planets (whether or not Mars is one of them isn't really a big issue) because they don't have the hubris to believe that there's anything so special about Earth as to believe that life could only emerge here.
Frankly, you can count me in that crowd. I'd be more surprised if it was somehow proven that there isn't life anywhere else.
To me, "fundamental questions" would be more like:
1. Is free will possible? If so, how?
2. How did the universe begin? If there was a "Big Bang" as popularly described, where did all the matter come from that expanded out of the initial singularity? If time did not exist before the universe began, how did the transition from state "no universe" to state "universe" happen, since - presumably - nothing can "happen" without time.
3. What is time?
4. Is space discrete or continuous?
5. Is time discrete or continuous?
6. Are there multiple dimensions of time, analogous to the multiple dimensions of space we know about?
7. Is our "4-D" world actually embedded in a higher-dimensional reality of some sort that we can't access/understand/see/etc.?
8. Is our world a simulation (ala The Matrix)?
9. How, exactly, do fields (electromagnetic field / higgs field / etc) permeate all of space and permit the existence of particles like photons or the higgs boson?
10. Is there actually a way to unify gravity and quantum mechanics?
11. What is dark matter? Where did it come from?
12. How will the universe end? Big crunch? Big freeze? Big bounce? The simulation ends and we all just disappear? Other?
13. Why is there any matter at all in the universe? The fact that there is implies a certain fundamental asymmetry to the universe, since if matter and anti-matter were created in equal amounts at the beginning, they should have annihilated each other leaving no matter behind.
14. Why are right-handed people more common than left-handed people?
15. Why does the universe itself appear to have a "handedness" property[1]?