I don't think there's anything inherently wrong with it, but there is still a certain stigma attached to it.
Posing this question on an internet forum is always likely to skew the answer more towards it being considered acceptable. Now, while I think it should be seen as a legitimate method of dating, I have to say that - like anything - it's relatively recent so a lot of people are still wary of it, or deride it as a poor excuse for "real life" dating.
I think the problem with it comes when people feel the need to justify why they use internet dating sites. Very few people say "I use it, so what?" or "yes", which should be the answer if it was broadly socially acceptable. Now, while that might not prove anything about how socially acceptable it is, it still shows that people believe there is a stigma attached to it. If you went out to a pub specifically to look for someone, nothing would be said, whereas to go on an internet dating site is still considered "weird" by many. Likewise, a lot of people are reluctant to reveal that they met on an internet dating site.
Personally, I think the stigma will be shed entirely and it'll be socially acceptable sooner rather than later, as soon as it's considered a natural way to look for potential partners by the majority, rather than indicative of social awkwardness; in the same way that people going online to shop instead of going out is no longer seen as them being a recluse.