I started watching Scrubs right before the beginning of the sixth season
I started watching Buffy in June
I started watching HIMYM right before the third season
I started watching House in the middle of the third season
I started watching Avatar in the middle of the second and third season
I started watching Bleach when they were around episode 110

Plus there are a bunch of shows I watched after they were completed. Of course, I started at the beginning after I realized I liked the show/decided to download a show and start watching it for shits and giggles based on no previous experience, but that is the place they were in the series when I started at the beginning.