With my earlier games: Border Reivers and Carpe Astra the mechanics definitely came first, and the same is true of It's Alive! one of the games I published on behalf of someone else. With Border Reivers I started trying to make a game like Mighty Empires that played faster and less randomly; I really liked the networking mechanic in the submission by Ted Cheatham that became Carpe Astra, though the theme changed quite dramatically. It's Alive! had been through several themes before I changed it to building Frankenstein's monster. So in my experience, mechanics first seems to work ok.
To further reinforce this, most of the many games I've started designing but failed to finish/lost interest in/couldn't get working started out with a theme first, which I tried to find mechanics that fit after the initial idea.
The theme acts as a hook for the game to interest people, hopefully enough that they want to play or buy the game. It's often possible to re-theme a game by picking something that roughly fits the mechanics and then tweaking the mechanics, action names or card wording to get the game to make sense with the new theme. In my experience it's often possible with very few changes to the game.
As I mentioned earlier this week after a conversation with The Wife a new game idea sprang into my mind almost fully formed. Theme and mechanics combined. Since then I've tweaked the theme slightly to distance it from a couple of similar new games (which I've added to my Christmas list so I can play them and ensure my game develops differently) and the mechanics have begun the long road of changes that will hopefully lead to a great game.
For me personally, I think the mechanics-first approach is the way to go. What are your experiences? Are you a theme-first or mechanics-first designer? How will my new game idea develop: theme and mechanics in lock-step, or will the theme change as time goes on? Stay tuned to find out!