First of all- Time travel makes a paradox. So- it would be logically impossible. However- If you could have a machine that only allowed you to VIEW the past, without being able to interact with it, then it would seem more feasible.
(it would most likely have to be like the dream-sequence in A Christmas Carol where he's visited by the Ghost of Christmas Past)
Now, if I had such a machine (the viewer), I'd relive my most dearest memories, and try to learn from past mistakes. I'd view my failures, and use them as tools for forging a better me- learning from mistakes, and remembering the good times, and also at times, I'd use it to look back to younger days when I was inexperienced at certain games, and laugh at myself. xD Or just reminisce. Personally, I'd also want to oogle my fuzzy itty-bitty kitties, back when they were the size of a potato.
...ALSO! With such a machine- I probably would be able to look at other moments in history- not just my own personal history. I could use it as a learning tool!
...And cheat on history tests. xD
Then again, if we had such a machine, we'd most likely have to change what's in the History books- considering there are probably a billion different mistakes all through there. Simply because in the far-back history, there were no records well-kept, and people made up stuff all the time probably. For glory and bragging rights most likely. And also- people tend to forget key details- it's just a part of nature. The brain isn't an unlimited storage device. And also- people lie and have delusions- so history as we know it today, probably by default, is full of holes and mis-information.