Well, that's quite an conundrum about time travel. I'm inclined to agree leave time travel alone. Maybe deploy the Prime Directive (Star Trek) in any case of time travel?
Seriously though, considering how we all got here and what would have happened if certain events in the past didn't happen, then we wouldn't be here at this moment in time.
WW2 was pivotal for so many people from all over the world. Had my husband's father not had different orders in the Navy, my husband wouldn't be here (ship was bombed)...so I'm glad the change of orders that took place kept my husband's dad alive, though I can't acknowledge that without saying my condolences for all the brave men that were lost that day and during the entire war.
My best explanation for time travel paradoxes is the multi-verse theory. That is, for every quantum or such interaction, every possible outcome occurs, in various alternate realities. So if I were to go back in time with the plans to erase my own existence, I'd simply spawn an alternate reality where I don't exist, but it would not affect MY reality, thus avoiding a paradox. The same can be said for those traveling into the future and back...
I have various other theories as well, but I'm tired and require slumber.
I really like your paradox theory @Zoldus. I could live with that and I wouldn't have to worry if I messed up something from the past while messing with time travel. So now you have to dish your other various theories someday