A poem's rhyme scheme can be anything the poet wants it to be, but here's a list of some of the more common rhyme schemes:
Keep in mind that this is just a list of some of the more common types of rhyme scheme. It's not a list of all the different forms of poetry, since the form of a poem is defined by more than just its rhyme scheme.
Dr. Seuss wrote many of his children's books in formal verse. The opening stanza of his book Horton Hears a Who, excerpted below, uses a simple rhyme scheme of coupled rhyme (AABB).
On the fifteenth of May, in the jungle of Nool,
In the heat of the day, in the cool of the pool,
He was splashing... enjoying the jungle's great joys...
When Horton the elephant heard a small noise.
In the excerpt of Frost's poem shown here, the B rhyme of the first stanza is taken up as the predominant rhyme in the second stanza, while the C rhyme in the second stanza then becomes the predominant line in the third stanza—making the rhyme scheme an example of chain rhyme (in which stanzas are linked together by rhymes that carry over from one stanza to the next).
Whose woods these are I think I know.
His house is in the village though;
He will not see me stopping here
To watch his woods fill up with snow.
My little horse must think it queer
To stop without a farmhouse near
Between the woods and frozen lake
The darkest evening of the year.
He gives his harness bells a shake
To ask if there is some mistake.
The only other sound’s the sweep
Of easy wind and downy flake.