Dictionaries call this word a verb, but it doesn't seem to behave like any other verb in the English language. Another question on this site calls it a “conjoined pronoun-verb combination”, which seems nearer the mark to me. What is the reasoning behind the dictionaries’ decision to label methinks as a verb?
Probably the easiest way to understand the syntax of methinks (in the present tense, that is; methought is its past tense) is by viewing it as saying “it thinks to me that”, where thinks here actually means seems, and that leading me is a “dative of interest”. Curiously, this is not the only verb to do this. Its synonym meseems (along with meseemeth also in the present and meseemed in the past tense) works exactly the same way, and for just the same reasons, too.
Like its synonym meseems, methinks is an archaic impersonal verb with two odd characteristics: despite its impersonality, it stands without a dummy it, and it includes a prefix me serving as an old “dative of interest”. That is the sort of dative that occurs when someone says “What happened to your old beater car?” and you say “What, that old thing? It broke down on me one time too many, so I junked it.”
Both meseems and methinks were originally written as two separate words: me seems and me thinks in the modern spelling, and in Old English variously me þinceþ, me þinceð, me ðincþ, me ðincð, and many others besides. Over the course of time, the original construction became obscure, many variant forms were seen, and they became fused into single words each.
The original ameaning of the Old English verb þyncan, ðyncan is not the one we use for think today, and indeed, this sense of think is preserved in modern use only in methinks alone. That original and now obsolete meaning of think was to seem or appear, which is exactly what it still means here. The seem meaning of think grew rarer after 1250, and disappeared some time after 1400 except in this frozen impersonal expression, methinks. For several centuries its written form varied wildly, because this sort of dative fell out of productive use and people became confused about what was going on and how it all worked.
So methinks is a real verb, albeit a curious one. It is in the present tense; its past tense form is methought. Its OED entry ponders the question of its curious syntax, which it calls “obscure”.
Pronunciation: Brit. /mɪˈθɪŋks/, /miˈθɪŋks/, /miːˈθɪŋks/, U.S. /miˈθɪŋks/, /məˈθɪŋks/
Inflections: Past tense methought Brit. /mɪˈθɔːt/, /miːˈθɔːt/, U.S. /miˈθɔt/, /məˈθɔt/, /miˈθɑt/, /məˈθɑt/.
Etymology: < me pron.1 2a + think v.1, originally as a simple syntactic collocation, in later use apprehended as a single word.
Now arch., poet., and regional.
impers. (Used with subordinate clause or parenthetically.)
a. In the present tense: ‘it seems to me’.
b. In the past tense: ‘it seemed to me’.
The set of forms provided is incredibly long, and contains several entries it thinks may have been transcription errors.
The OED2 has this extended note on its etymology:
As think v.1 did not, exc. in this phrase, survive beyond the 14th c., and had no very wide currency after 1250, the syntax of methinks became obscure. Hence it underwent various alterations of form. The verb being supposed to be think v.2, it followed that it ought to be in the first person; hence the form me think, in which probably the pronoun was still correctly apprehended as a dative. In the 16-17th c. there occur the forms my think, my thought(s, which are attempts to obtain a normal syntax by taking think, thought, as sbs. The curious form methoughts, used in the 17th and the first half of the 18th c., prob. owes its s to the analogy of the present tense methinks.
It then goes on separately document in the present tense all of me thinketh, methinks, methink, and my thinks(s, and in the past tense all of methought, methoughts, my thought.
The OED3 has an even longer etymological note, of which this is just the beginning:
Although the impersonal use of think with indirect objects other than me persisted until the early 17th cent. (see think v.1), the syntax of this collocation seems to have become to some extent obscure already in Middle English. Hence it underwent various alterations of form.
The present tense (β) form me think apparently shows substitution of the first person singular inflection, perhaps resulting from identification of the verb with think v.1 (compare Middle English forms with thenk, þenk, etc.); the pronoun was perhaps still apprehended as some kind of indirect object. The form me þunch in Owl & Nightingale (Calig.) 1649, 1651 (see quot. c1275 at sense aα. ), is probably to be regarded as a variant (with inverted spelling of h for þ) of the α form me þuncþ found elsewhere in this text rather than as an early example of the β forms (the expected first person form would be þunche). The Middle English forms me þinchez (c1300 in texts in MS. Laud Misc. 108) and me þinkez (c1330 (c1250) Floris & Blauncheflur (Auch.)) probably show use of the graph z for /θ/, rather than γ forms.
The reason it doesn't behave like any other verb is that there is no other verb like it — or at least, no Modern English verb.
It’s an Old English verb which means “it seems to me,” and although it survives to the present (OED has a 1991 citation), it’s listed as “archaic, poetic and regional”.
It’s also listed as an impersonal verb (a verb with no subject), used with a subordinate clause or parenthetically:
Methinks I hear some frowning warrior say, “With such unmanly thoughts, away! away!” [J. Cottle, Poems, 1796]
Ha, ha—go away! ’Tis a tale, methink, Thou joker Kit! [T. Hardy, Wessex Poems, 1898]
Dictionaries list it as a verb because that’s what it is.