Good way:
Buffy
Batman TAS - This one REALLY exceeded the great expectations I already had!
Power Rangers - I stopped being a regular viewer after In Space, but returned for a short time when Tommy was on Dino Thunder series and the Forever Red episode. I really liked how the show stresses the importance of friends, teamwork, overcomign fears and obstacles considering the age group the show's aimed at.

I'll add more as they come to me.

Supernatural.

The pilot was really good but a large part of the remainder of the first season was just rehashed plots from existing horror movies. I continued watching because I'd bought the first 3 seasons in one box, and thankfully it got much better. I've seen up to the end of S5. Really need to get the rest.

When Castiel came into it, I got completely hooked. He's awesome.

Once Upon a Time

I don't like TV series but OUaT is great.

I almost fell in love with Rumplestiltskin... Hook must die, he's just an idiot.

Farscape. I thought the first half of season 1 was ok, but then the second half (and all the rest) was brilliant!

The Big Bang Theory. I'd seen adverts for it but didnt think much of it, but I caught an episode when visiting my sister and I was hooked.

The Big Bang Theory. I'd seen adverts for it but didnt think much of it, but I caught an episode when visiting my sister and I was hooked.
This is how I discovered Animaniacs. But, not the "visiting my sister" thing.