The first time around I didn't write any thank you letters and I didn't match. The second time I didn't write any and I matched.
From my experience being around residents and attendings a lot during my research year and hearing them talk about the match process constantly, is most faculty don't really care about thank you letters. Most faculty, especially chairmen and PDs, just think of it as part of the job. If you want to make a real impression, being seen as much as possible is much more effective than a thank you letter. Ie. conferences, grand rounds, etc at your home program, and rotating/second visits at other programs.
That being said, residents really seemed to be swayed by thank you letters. I saw several hung up on message boards and such in conference rooms and call rooms. Some complained when rotators didn't send any correspondence to follow up.
Of course, I also heard residents make fun of rotators who sent letters that kissed too much butt, so there's no hard and fast rule...