Is it possible for a virus (or other parasite) to make its host crave sex? Absolutely and easily. Sex drive is pretty much driven by hormone production and it's trivial for a parasite to tweak the production of a hormone or two. Testosterone would be a likely candidate (it increases libido in both women and men) and maybe something that reduces inhibitions. Easy-peasy, and your infected are horny all the time.
Is it possible for such a virus to succeed this way? Well, that's a lot harder, because it relies on the partner not recognizing the presence of abnormal behavior. Humans tend to be pretty picky about their partners, relatively speaking, and sexual attraction takes time, subtlety, responsiveness, and intelligence. That's brain-stuff, not chemistry-stuff, and parasites aren't very good at brain stuff.
Of course, a particularly physically attractive host might be able to spread the parasite a fair amount anyway just by being readily available - but since particularly attractive hosts tend to be pickier about their partners, the chances of such a host picking up the parasite in the first place is much lower. So it's unlikely for the parasite to ever get off the ground just turning its hosts into sex zombies.
Nevertheless, it's not impossible, if the parasite is subtle in its machinations. There are some studies that suggest that Toxoplasma gondii (like you'd expect any other parasite) might make women more promiscuous, and it might be capable of sexual transmission, although this isn't its primary route of infection (also, humans aren't its main host). But studies are inconclusive, and for good reason - after all, if it was obvious, it wouldn't be as effective, would it?