We did not buy a new mattress, although we also haven't put DD2 in her crib full-time yet. I talked to my pediatrician about it, and he didn't feel like the research on reusing mattresses was particularly compelling, which was honestly my feeling as well. As long as your mattress is still firm, clean (no rips, tears, or persistent stains), I would consider reusing it. If you have any concerns about your mattress condition though, I would not hesitate to buy a new one.
DD1 10/2010
DD2 8/2013
And expecting DS1 10/2016