I keep seeing "me thinks" written on this site. The correct way to write this archaic expression is "methinks". For explanation, here is a piece of wikipedia:
(I did not want to type this out myself for fear of invoking Muphry's Law).While the dative case is no longer a part of modern English usage, it survives in a few set expressions. One good example is the word "methinks", with the meaning "it seems to me". It survives in this fixed form from the days of Old English (having undergone, however, phonetic changes with the rest of the language), in which it was constructed as "[it]" + "me" (the dative case of the personal pronoun) + "thinks" (i.e., "seems", < Old English thyncan, "to seem", a verb closely related to the verb thencan, "to think", but distinct from it in Old English; later it merged with "think" and lost this meaning).
The dative case also survives, albeit rarely, in the ethic dative, used to express one's interest in a matter. This only occurs with pronouns. For instance, in the sentence, "Cry me a river," "me" is used to express the speaker's interest in the action.