Prime Example: Firefly.
Firefly was an amazing series. We're talking the Wild West with space ships. For those of you unfamiliar with this little piece of awesomeness, it was a short-lived Joss Whedon (of Buffy the Vampire fame) creation that aired on Fox in 2002, starring Nathan Fillion (now in Castle), Adam Baldwin, Jewel Staite, and Summer Glau (among others). While it was cancelled before it even finished airing all 14 episodes, it garnered enough fan support to make the follow-up movie Serenity a reality in 2005. It recently aired on The Science Channel as one of the best science fiction series ever.
Its early demise remained a mystery to me until I read the early critical reviews of it. They lead me to believe that general reactions went something like this:

Yeah. Apparently, the mad mix of sci-fi-Western-comedy-action-drama didn't sit well with some people, who felt they were an unholy concoction forced together via Whedon's insane genre alchemy. And yet, I never once gave it a second thought. The world of Firefly felt complete and whole to me, with nothing out of place and nothing forced or strained. I didn't care about some cliche metaphor about the final frontier and the Wild West. I just sat back and enjoyed the ride.
You see, by the time Firefly came along, I'd had a good five years of anime like Cowboy Bebop, Outlaw Star, Trigun and Gundam Wing to acclimate me to the idea of the space cowboys, rough-and-tumble frontier planets, and complex interplanetary politics. As for mixing genres, well, that's practically par for the course in anime and manga. Just ask Rumiko Takahashi or the CLAMP team. Mixing comedy, drama, romance, and political intrigue is pretty much commonplace, so I don't think anything of it when an American TV show gives it a try.
Anyway. This is what I get for watching old TV series and checking out their Wiki pages afterwards. But it does beg the question: DOES mixing genres like that still bother a lot of people, or has that changed in the past ten years?
Judging by some of the shows slated to air this fall, I may have an answer soon...