"A Valediction: Forbidding Mourning" is not written in a specific, named form. But that doesn't mean it isn't formal. The poem follows a very strict structure of its own making and shows remarkably little deviation. It is composed of nine four-line stanzas called quatrains, each with an alternating ABAB rhyme scheme.
The meter is iambic tetrameter, which may or may not mean anything to you at all. An iambic meter means that the syllables alternate between unstressed and stressed syllables. Tetrameter means that there are four stressed syllables per line. (Tetris gets its name from its shapes made up of four square blocks.) This means that each line has eight syllables. For example:
Though I must go, endure not yet. (22)
If you read this line aloud (go ahead, nobody's looking), you should hear four iambs in a row: da-DUM, da-DUM, da-DUM, da-DUM.
Now, almost every formal meter has lots of variation, but this poem sticks closely to its pattern. In part, this helps the reader out. We've got enough to figure out just trying to understand the poem's argument. We don't need a bunch of trochees and spondees freaking us out. But there is some variation and it's worth noticing.
The first line has an insignificant little deviation—it's got an extra unstressed syllable in the word "mildly." This is very common in metered poems and so it's really not safe to read anything into this, but you could argue that crowding a line with extra unstressed syllables de-emphasizes the stressed syllables and makes this nice, peaceful line even peacefuller… uh, more peaceful. The same thing happens in lines 17.
The beginning of stanza 3 reverses the stress on the first two syllables so that the word "moving" gets extra oomph, which makes sense, because we're talking about an earthquake. The next stanza loses its first syllable altogether, letting the first line open with the thudding stressed syllable "dull." Line 14 and 15 have the first hard enjambment, or contrast between the grammar of the sentence and the line break, and that gets extra stressed with the reversed beginning word "Absence."
Stanza 6 has the most variation in the poem. First, the opening line reverses the stress to throw emphasis on the word "souls." Then there is a missing syllable in line 23, which hammers home that whole idea of a "breach."
To sum up then, this poem sets its own rules when it comes to form and meter, but it does a good job of playing by them. Only when it wants to emphasize or mirror its content does it break those self-imposed boundaries.