Just as a caveat, it depends on what happens to your phone (If you need to return it in warranty). There are ways to unroot and return your phone to the stock condition. http://rootyourdroid.info/Rooting has its pros and cons. It brings a lot of benefits but the Huge downfall is you lose your warranty on your phone. If you root neither Verizon or Asurion will replace your phone if something happens to it.
Rooting allows you to run custom roms which look awesome as well as overclock your processor and wifi tether. There are a lot more things rooted users can do but these are the most popular things.
Of course, if your phone is messed up too badly then that might not be possible. But I have rooted and unrooted (returned my phone to stock condition) so it's not that difficult. The wifi tether is really nice for more than one computer (especially if you want to tether a computer running linux).
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