Others in this thread have already covered the major points, so I'll be brief. Don't make their entire life and personality revolve around the tragedy, but don't just mention "oh no tragic history!!!" and leave it at that either. Find the middle ground where real people end up after experiencing tragedy; there's a lot of room for differences between the two ends of the spectrum. Strive for realism in emotional responses, because that's what will speak to people. Just avoiding the traps of overplayed eternally brooding tragic characters or emotionally dissonant super happy on the outside to mask sadness type characters will do a lot for avoiding the cliches associated with tragic histories.

However, avoiding cliches just for the sake of avoiding them isn't always a good thing. A lot of cliches have acquired that status because they're solid story devices or because they're based in the reality of how people react to things. For instance, in direct relation to the tragedy thing, a character having a mental/emotional breakdown after experiencing a major loss is extremely cliche, but it's also extremely realistic and to maintain believability you would probably have to explain why your character did not have such a reaction. There's plenty of wiggle room in realistic depictions of emotions and reactions and such for the sake of making good fiction, but it's a good thing to keep in mind if you're trying to make solid characters that readers will appreciate and relate with.

Oh, also, originality is not in and of itself a good or bad thing, nor is unoriginality. Both assessments are comprised of comparing your work to that of other people, which is usually not a great thing to do. You should instead strive to make the best possible thing you can, regardless of what others have done. If someone else thought of it first, so be it, your writing style and the situations you put that character through should be enough to make them markedly different in the end anyway, so who cares? In the end, if you're not trying to sell whatever you're writing, the only thing that matters is if you like the character and enjoy writing them. Focus on that instead of trying to be unique and you'll be happier for it.