I can't say that "I like anime", because really, I don't.
I don't hate it either. I actually watch a fair bit of anime.
The thing is though, it's such a BROAD term... anime in general is just like saying "I like tv". Whot kind of tv? There's dozens, if not hundreds, of different types of programs out there. Sailor Moon isn't remotely similar to Hellsing, for example. Princess Mononoke does not really compare directly with Ninja Scroll. There's many genres within anime.
Some rare people find that, just because it's japanese animation, that's all they care about.
Most people, however, will find a distinctive difference between watching Evangellion and Pokemon.
As such, I have no particular "ZOMG I LURVES ANIME!" in general, however, I do recognize that there's a great many shows that are good in it. And there's a great many that FLAT OUT SUCK BAD. I liked Inuyasha, or Excell Saga, but I thought Akira was one of the dumbest movies I'd ever seen, and I normally like the themes it covered.
Such is the way of things though; yeu can't just like "all" anime. It's too broad reaching. It's not a genre... it's a cultural slant upon OTHER genres.
Anime tends to have a more in depth, emotional plotline, and usually spans across multiple episodes as a steady progression rather than singular episodes. These are typically good traits, but often, these same anime are derived from a manga (graphic novels basically), and alot of the time there's either stuff edited out, compressed for time, or just fluff and filler added while they wait for the next issue of the manga to be released... which's like trying to produce a tv show without a script... hence why dragonball Z ended up with such immense filler time - they were waiting on the script but still had to produce a show

; Of course they're supposedly remaking that series and editing out 2/3rds of it which was apparently all filler o.o
In any case, I don't mind watching anime, and on average it tends to be better than most north american shows, due to the more in depth plotlines and stronger character development across the shows. There's alot of total crap, too though, that never gets translated and we never see over here because it's total crap XD
I'm not going to pretend 'anime' is magical and somehow 'better', the vast majority of anime sucks. Just as the vast majority of hollywood movies suck. Yeu can't lump it all together, really. Individual shows, though, can be quite good, and I'm fully accepting of anime as a valid adult form of entertainment on par with live action shows. Yeu can do alot of stuff with animation yeu can't with live actors, no matter how large yeur special effects budget may be. As anime doesn't have the problem of being viewed as "for children only", it's far easier for it to show adult themes, such as betrayal, death, and so on which yeu don't normally get in cartoons over here.