Good ol' Sitemeter never fails to yield its share of fascinating factoids. For example, earlier today some brave Canadian Googler found my blog by searching for, and I quote, "think vs believe semantic difference".
Having nothing but love for my readers, I think it only fair that I might attempt to address the deep and profound "think" vs. "believe" distinction. Let us take the following two sentences as our minimal pair:
1. Willy thinks that the wine is good.
2. Willy believes that the wine is good.
In both (1) and (2) above there is a verb of cognition (e.g., FrameNet frames Awareness, Certainty) which takes a clause as its complement. The difference lies in the nature of the truth value predicated of the complement clause by the matrix verb (think vs. believe).
We could couch this truth value predication either in terms of a) epistemic modality or b) evidentiality. Either way, the verb "think" denotes lesser confidence in the truth of the complement clause than the verb "believe" (and they both denote less confidence than the verb "know").
So (1) should be interpreted as meaning Willy has weak confidence in the belief that the wine is good, whereas (2) should be interpreted as meaning that Willy has strong confidence that the wine is good. So the difference between "think" and "believe" is one of degree in confidence of the truth of X (where X is a proposition...which is a tad redundant if you take it to be the case that only propositions have truth value...)
You'll have to try the wine yourself to decide if Willy knows his wine or not.