I realize it's not very shocking to say that two teams, currently in the Elite Eight will end up getting to the Final Four, but this is more than just a prediction, it's an educated guess based on research!
Last night, while watching Kentucky hang with Ohio St. I thought back about other 4 seed over 1 seed upsets, and how often the team that pulls the upset ends up winning their next game and making the Final Four. So I looked into it, and as it turns out the last 10 teams to beat a 1 seed in the Sweet 16 have gone on to the Final Four. The last time it didn't happen was 1995 when (4) Virginia beat (1) Kansas but then lost to (2) Arkansas in the next round. The teams in question have always been a 4 or 5 seed and in 7 of the 10 cases they have gone on to beat higher seeds in the next round.
This year two teams fit the description, the aforementioned Arizona and Kentucky. They're facing a 3 seed and a 2 seed, respectively, but as I just explained, that shouldn't really matter.
So why does this happen? I would argue that the fragile young men that typically make up a college basketbell team ride the confidence gained from their win over a top team to another victory two days later. Plus if they get to the Final Four they get to visit awesome places like Minneapolis, St. Petersburg or Indianapolis.