I'm not sure if there is a site that offers foolproof verb conjugator. dongsa.net has been there for a while, and I just checked verbix.com mentioned by Susanne. Both sites seem to use the same engine underneath and fail (list wrong forms) on some irregular verbs. For example, they don't seem to have anything to distinguish between verbs and adjectives. They list 부드럽는다 for 부드럽다, which is never used (it should be 부드럽다, the same as its base form). It's in a way understandable as it's no easy task to get all the conjugations right. There are homonyms that conjugate differently, for example, which would be quite difficult to get right. 1. 곱다(pretty - ㅂ-irregular) -> 얼굴이 고와요. 2. 곱다(hand or finger feels numb from cold) - regular) -> 손이 곱아요. dongsa.net lists #1 while verbix.com lists #2. Since the #1 meaning is much more widely used, dongsa.net is better on this example. It also indicates the irregularity of verbs which verbix does not. Other than that the two sites function very similarly, and it seems most (over 90 percent) of their output is correct.

You might try verbix.com but I'm not sure if it's accuracy. Maybe a native speaker can verify its worth for both of us.