Like the people above have said, good characters, writing, plot, art direction, animation quality, enjoyability all come into play.
It's got to be the right amount of that stuff. Compensation and balance are what's important. I can overlook an art style that I normally wouldn't enjoy if it has strong writing and characters (Kaiji, Clannad, Steins;Gate, in these cases I ended up embracing the art style later.) On the other side if the story is bad sometimes I can overlook that if it's a joy to look at (Panty & Stocking with Garterbelt). So in most cases it just comes down to if the show has enough good things that it outweighs it's flaws and becomes great.