Cycling is a sport with a doping problem, but it is also the sport that tests the most. Lance was tested more then any other athlete the 7 years he won the tour and has never failed a test. Is that proof he never doped (probably EPO or blood doping, not steroids)? Of course not. Does it make it unlikely? Yes. Cycling is not afraid to suspend even the biggest names when they are caught so they wouldn't hide positive tests for Lance. Further, he was hated by ASO and they would have liked nothing better then to have removed him from any of his wins.
His rivals were caught doping trying to beat him (Operación Puerto) and he still wiped the floor with them for 7 years and came out of retirement to podium. If he can podium at his age, after 4 years off, without proper pre-tour preparation because of the accident and broken collarbone, and supporting his team mate is it that much of a stretch that while in his prime he won them clean? Oh, and all this after nearly dying because of cancer. Having a second chance at life is great motivation and he has stated many times that without that motivation he would most likely have never put in the effort needed to win once let alone seven times.
Why would we believe someone who spent 4 years lying to the entire world and wrote a book pleading his innocence only to admit he lied the whole time? He also solicited donations from fans to fight the allegations and suspension that were, in the end, completely justified.
Unlike baseball where rampant drug use was ignored and positive drug tests swept under the rug (A-Rod anyone) cycling at least addresses the problem. Michael Rasmussen was removed from the TdF and fired from his team for merely lying about his ware-abouts while training because it was seen as a ploy to avoid out of season testing, and he never even failed a test.