I've got four different songs in my MP3 collection entitled "Heart and Soul", by Joy Division (1980), Big Country (1983), Huey Lewis & The News (1983), and T'Pau (1987). I've also got four different songs entitled "Money", by The Beatles (1963), Pink Floyd (1973), Buzzcocks (1979) and Suede (1993).
I think four is my personal record for same-titled different songs: there are a few threes (including "Heaven" by Talking Heads, Bryan Adams, and Robyn Hitchcock & the Egyptians; "Mother" by Pink Floyd, The Police, and James; and "I Believe" by Buzzcocks, Tears For Fears, and R.E.M.) and a whole bunch of pairs. Unsurprisingly, the duplicate titles are mostly either one word ("Limelight", "Rain", "Changes") or cliché phrases ("I Should Have Known Better", "Head Over Heels", "The Power of Love").