If they're good tattoos, fuck yeah. Lots of assumptions and stuff here that I disagree with, but I'll just say that as usual I agree with Mora.
For the record, most of the people I know who are covered in ink are not trying to be trendy- they truly love tattoos and are doing what makes them happy. Yes, tattoos are way more common and socially acceptable now, but a lot of that ink is boring shit that somebody picked off a wall or stole from somebody else's idea. A woman who can rock some interesting ink, on a sleeve or anywhere, is extremely sexy to me (same with men).
I have nine or so tattoos, most of them fairly big (no sleeves yet because I am debating on that with work-related stuff). Any person who says my body is less attractive because of them is not somebody I'm interested in dating/boning, and their opinion means pretty much zero. I have no interest in dating people who think they have any say in what I do with my body in general, so a partner being critical of tattoos would not stick around very long.
I personally don't like face or chest tattoos, but would never tell a partner those things are unattractive or try to talk them out of doing something they really wanted to do (I mean, unless it was a giant Majesty logo chest piece).
And Barto, totally disagree that a healthy body can't also be a tattooed one.
Side note: my ink makes me feel much better about my body and gives me added confidence. I think it's beautiful work, which is great because my feelings on it are really the one ones that matter in the end.