For me it really depends... I mean, if the art is terrible, I'll probably give it a go regardless and, depending on how the rest of it's content, I'll decide whether to continue or not. An example of this is Ping Pong the Animation. It's almost an undeniable fact that the art was terrible, but the script and story were (to me at least) well written which made the anime, though it's art was bad, enjoyable. However, I'm sure there are anime that are poorly animated and the rest of it's content isn't very good either. An example of this, for me, was Dirty Pair. I wouldn't say the animation as horrible, but, as it's older, it definitely wasn't appealing when compared to more recent titles. To me, the plot and comedy weren't the best either so I gave up on watching it (for the time being. Being the completionist that I am, it'll get finished at some point).
I also feel that this can work in the opposite manner as well. For example (I know this is a hotly debated topic on other sites) I personally didn't like Sword Art Online that much, though the art was stunning. I felt that, other than it's art it didn't have much going for it, which is why, just like Dirty Pair, I ended up putting it on hold for some time (though, unlike Dirty Pair, as of now, I have completed Sword Art Online).