Well I can be a little sarcastic and raise a counter argument to a truly great article found here:
Paradoxes can be solved by science and janitorial aids.
That's right folks, if you do manage to create a paradoxical double of yourself you're safe in the knowledge that the duplicate is always doomed. This could be especially handy if you need to pull the ultimate escape and get away from it all. It might be a pain trying to prove you're really alive and that other body was just a spare later on but why worry about that now, you have a time machine.
Narcissism - how much do you love yourself. Why not pop back to last night and find out? It also takes care of all those annoying little setbacks when considering a threesome. If you don't want to include someone else why not have two of you? I mean if you end up enjoying yourself in the process it's basically masturbation right?
In a well thought out, well planned universe there should be back up plans for time travel. Reality hasn't noticeably ripped itself apart so if space-time travel has been invented we can assume it's all fine and good. But if you do decide to go for a quick jaunt to the past, don't do anything unless you were meant to do it. Then whatever you do, don't not do it.
Spare parts - let's face it the human body is pretty fragile. Why wait on transplant lists when you can just nip back, grab a double of yourself and get a perfect match? Remember point 1, that double is doomed anyway so don't worry about it and just enjoy that kidney for a few more years.
Ok so not a set of well thought out and planned examples but still is reality all that great when it all comes down to it. If you do end up playing a hand in its downfall at least you'll be known as the harbinger of the apocalypse or the guide to some kind of golden Eutopia of reality 2.0. Either way it's more recognition than you'll probably get now.