I look at the toys first to make sure the tags aren't loose, but no, I don't cut them off. In fact, DS loves the tags, they are his favorite part of the toy! He also chews on them, but I just make sure he's supervised.
We've started cutting off any tags that are longer than an inch... especially since she started shoving them half-way down her throat a few months ago! Anything shorter than that, unless it's starting to come off anyway, I'm not too concerned about.
Re: tags on toys
This exactly. DS loves to feel the tags too.