Note-some links might contain explicit lyrics, if you're offended by that sort of thing.
A few returning players have opted to keep the songs they used last season.
Nick Markakis- "Deliverance" Bubba Sparxx (IP/O's/S)
Adam Jones- He used four songs last year and is bringing back the last two: "California Love" 2Pac (IP/O's/S), "Keep Their Heads Ringin'" Dr. Dre (IP/S)
Matt Wieters- "Barefoot Blue Jean Night" Jake Owen (IP/O's/S)
Jake Arrieta- "Bad Company" Five Finger Death Punch (IP/O's)
Jim Johnson- "The Pretender" Foo Fighters (O's/S)
And here's the rest of what I have so far:
Nolan Reimold- "Wolfpack Theme Music" NWO (seems to be a wrestling thing) (IP/O's/S)
J.J. Hardy- "Flower" Moby (IP/O's/S)
Mark Reynolds- "Country Boy" Aaron Lewis (IP/O's/S)
Chris Davis- "Mystery of You" (O's/S) & "Watch You Crawl" (S) Red
Wilson Betemit- "Te Pue Cuida" El Batallon (O's)
Robert Andino-"Hustle Hard" Ace Hood ft. Rick Ross & Lil Wayne (IP) "Go N Get It" Ace Hood (S)
Endy Chavez- "7 Locas" Don Miguelo (O's)
Ryan Flaherty- "Wild Rover" Dropkick Murphys (O's/S)
Nick Johnson- "I Got 5 On It" (Instrumental) Luniz (IP/O's)
Ronny Paulino- ???
Tommy Hunter- "Where I Come From" Montgomery Gentry (IP/O's/S)
Jason Hammel- "Panic Switch" Silversun Pickups (O's)
Brian Matusz- "VooDoo Child" Jimi Hendrix (O's)
Wei-Yin Chen- "Just A Dream" Nelly (O's)
Luis Ayala- "Jefe de Jefes" Los Tigres Del Norte (IP/O's/S)
Kevin Gregg- "Country Boy Can Survive" Hank Williams Jr.
Matt Lindstrom- "When the Levee Breaks" Led Zeppelin (IP) "Fireman" Lil Wayne (S)
Darren O'Day- "Thickfreakness" (O's) "Lonely Boy" or "Howlin' For You" (S) The Black Keys
Troy Patton-"Glitter" Ghostland Observatory (O's/S)
Pedro Strop- "Ponte Tu Chaleco" Secreto El Biberon
Both sites also have songs listed for players who are either injured or didn't make the team out of Spring Training, so I obviously haven't been able to confirm the following songs.
Brad Bergesen- "One" Swedish House Mafia (S)
Zach Britton- "Closure" (O's/S) or "Alive" The Continuums (I'm guessing that he's friends with someone in the band since their songs only have like four views on YouTube)
Dana Eveland- "Symphony of Destruction" Megadeth (S)
Zach Phillips- "Stranglehold" Ted Nugent, "When the Levee Breaks" Led Zeppelin, or "Those Shoes" The Eagles (S)
Chris Tillman- "Take It Outside" or "Kick It In the Sticks" Brantley Gilbert (S) (He used the latter last year)