warning: incoming cornfest
Well honestly, I wouldn't want to go back to the past or fast-forward into the future. I wouldn't want to go into the past for any reason. Anything that I've experienced that is worth remembering has been committed to memory, and the things that I've forgotten are most likely not worth remembering in the first place. I wouldn't want to go back into the past to change anything either, as the events that have occured in the past, both good and bad, have shaped who I am today. Sure, I've done some pretty bad or embarrassing things, but each of those things have been an experience and a lesson which I can learn from now, and going back to fix what I would see as a mistake would mean reversing events that have shaped me.
As for travel to the future, I wouldn't want to travel into the future either as I would want it to be a surprise - similar to how I wouldn't go and watch the last episode of an anime or TV series before I've even gotten half way through it. I wouldn't be able to understand what's going on if I skipped so far ahead. New people would be around whose backstories I've missed. Events would've led to personality changes and lifestyle changes which I also would've missed. As curious as I am to see what kind of person I become and what situation I'd be in a few years down the track, I think my curiosity would be better satisfied if I were to just live my life as per normal and let the future come to me naturally.
However, travelling forward or back through time to a point where I wouldn't actually be existing is a different situation altogether. It would satisfy my curiosity to see gaps in history that haven't been recorded in history books, or the more dubious parts of history which weren't ever fully understood. It would be really interesting to see what really happened at many historical events, and I wouldn't be able to experience these events any other way. I wouldn't try to change anything, of course - who knows how this would affect the present. I also would love to travel many years into the future, to a time long after I've died. It would be interesting to see how the world would be, and I wouldn't be able to satisfy my curiosity about this any other way.