Hughes does indeed use free verse in most of his poems, as the previous poster states, but "Harlem" is at least as structured as many of his other pieces and, I believe, can be analyzed more fully in terms of its meter and verse form even if we still agree that it, too, is an example of free verse.
Let's begin by looking at lines 1-5. The third and fifth lines have end rhyme ("sun" and "run"). We can call this pattern "alternating rhyme" and can spell out the pattern as XAXA, using X to indicate that the second and fourth lines don't rhyme. We may also note that lines 1, 2-3, and 4-5 each form a single question. Additionally, we may notice a number of repeated sounds within the lines, including alliteration in line 1 (“dream”/”deferred”), line 2 ("does”/”dry") as well as internal off-rhyme in line 3 ("raisin" and "sun" end similarly), line 4 ("fester" and "sore"), and line 5 ("then" and "run"). Finally, we may note that lines 2-5 can be read out loud to contain two stressed syllables per line, a pattern which we can loosely call "iambic dimeter." ("Iambic" is the natural rhythm of spoken English, with alternation between unstressed and stressed syllables. It’s no surprise that a poem in free verse would lean toward iambic meter. Of course, in this poem, we have to put a little more stress than we normally might on the word "then" in line 5 in order to find two stresses in this line.)
Lines 6-8 maintain many of the same patterns that we found in lines 1-5. Again, we see alternating end rhyme (“meat” and “sweet”), a set of questions, alliteration and other repeated sounds within lines, and two stressed syllables per line.
Lines 9-10 present one possible answer to all the questions that have been asked up to this point in the poem. Although this poem is not at all a sonnet, this section makes me think of the “volte” (or “turn”) in the traditional sonnet, the switch from question to answer or from problem to solution. The final line is returns to the form of the question but we may read this line as containing a new, frightening possibility. The failure to realize the dream (perhaps meaning racial equality in this poem) may result not just in silent suffering but in outbursts of violence.