Season 1-2 is fun and extremely cracky, but really bad. It's the kind of show that's fantastic if you're drunk while watching it. Season two so that sucked.
Season 3 were much better written, but it's such a depressing season it might not be worth watching. I watched the whole season in one evening, and afterwards I cried for two hours, said "that was fucking awesome" and then I never watched it again. It's hated by a large part of fandom, because it and because it's over the top depressing.

That Torchwood is one of the Doctor Who spin-offs helped build up a fan base for the show, and then the slash pushed the fandom to the next level.

Torchwood is very different than Doctor Who, but still fun to watch. Like, the latest episode of DW had a sword-fighting Victorian lesbian couple.
If those characters had instead been in Torchwood, they'd also fight crime! using the power of sex! and then everything explodes!!! - so that is the basic appeal of Torchwood. When you're drunk it's the greatest show on the planet.

I mean, there's canon mpreg within the first five minutes. That's amazing. And the fourth episode has a bikini-clad cyborg fighting a pterodactyl!