So I just answered the question "Are rappers musicians?" on Facebook Questions, and I'd like to share my answer on here!
Music is defined as (paraphrasing http://www.merriam-webster.com/dictionary/music), combining tones and sounds for artistic value.
That being said, rappers are very much musicians, as their contribution to a song is integral to not only a song's effect but also its meaning. Rappers rely less on tones and more on rhythms, and as many people have already pointed out, so do drummers - musicians. Rappers use their voices to produce their music, just as every other singer or vocalist does. Although the don't focus on pitch (but they do use it), their tones, timbres, and inflections are used and even celebrated. This is why B.o.B sounds different from Eminem sounds different from Lil' Wayne.
An interesting point on drummers - tabla players in Indian Classical music have onomatopoeic syllables to describe different kinds of strikes or hits. They are expected to be able to pronounce them as fast as they can play them, and sometimes even perform this way.
http://chandrakantha.com/articles/indian_music/bol_percussion.html
One point of argument may be in the repetitive nature of most rap songs. Cyclic music, although definitely found in Western music, is even more common in other musical traditions. In these styles, the musical piece is appreciated as more of a repeating melody with subtle or not-so-subtle variations thrown in; much like rap. I'm thinking particularly of Shona, Hindustani, and Gamelan music.
http://www.britannica.com/EBchecked/topic/147944/cyclic-form
Although rap lyrics can definitely be considered a subset of poetry, it's hard to imagine most rapper's style applied to other poetic forms such as haikus or limericks. While a rapper can and sometimes do rap without music, their lyrics are specifically intended to be performed withinstrumental accompaniment. This separates rap from Spoken Word, which is a definite form of poetry.
https://www.msu.edu/~miazgama/spokenword.htm
They may not be musicians like Rossini or Mozart as one answerer said, but I would argue that they may be. Mozart and and the like gained their popularity by how their arrangements of tones and sounds appealed to the common listener, which is exactly what guys like Jay Z or Snoop Dogg are doing. Time will only tell how long their music will last - don't forget that Mozart was the "sex, drugs, and rock-and-roll" of his time and genre, and Stravinsky's Rite of Spring essentially caused a mosh-pit at it's debut.
http://www.imdb.com/title/tt0086879/
http://www.npr.org/programs/specials/milestones/991110.motm.riteofspring.html
With all of that being said, I firmly believe that rappers are musicians.
