Outside non-canon material, I have never seen, or even heard a mention of the Marines in Starfleet. It seems Rene Auberjonois' character in Star Trek VI, Col. West (the officer who presents the extraction plan for Kirk and McCoy to the UFP President) was supposed to be a marine. However, in TNG, we hear nothing about them.
The last two seasons of DS9, which woould have been the perfect time to introduce them, make no mention of them. The episode "The Siege of AR-558" shows Starfleet officers -- regular ones like starship crew -- battling the Jem'Hadar, not combat-oriented operatives.
This leads me to conclude that Starfleet does not maintain a marine contigent, counting on cross-training to provide its officers with batle skills.
What everybody else think?
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"As long as you can laugh, you are not
defeated."
–- Jack Vance