As others have said, worn tires could definitely induce steering issues. Also be sure to check your tire inflation. If you've ever been in a front-end collision, then that could also contribute if it wasn't fixed properly. My factory-original set of tires didn't last very long because the alignment was messed up from the factory, which basically killed the tires after 5000 miles. I screamed and the dealer ate about half of the cost of replacing them.

FYI, I recently replaced my aging Yokohama AVS-ES100's with Michelin Pilot Sport II's. In addition to being very smooth running and all that, they're a very different sort of directional than traditional directional tires. They have no particular preference for which way they're rotating, but they do have an "inside" and "outside" (i.e., left-to-right tread asymetry). This means you can legally rotate them left-to-right, since the "outside" continues to face out.