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If you don't care about the original sorting order (or if you want it sorted), use Union:
Union
Union@{a, 1, 5, 3, 5, x^2, x^2} (* {1, 3, 5, a, x^2} *)
{1, 3, 5, a, x^2}
If you don't care about the original sorting order:
Union@{a, 1, 5, 3, 5, x^2, x^2}
If you don't care about the original order (or if you want it sorted), use Union:
If you don't care about the original sortingsorting order:
If you don't care about the original sorting: