This song was written by Van Morrison, and first recorded in 1967.
Brown Eyed Girl definitely reflects the talent of the ever-loved Morrison, and as with any popular song, over the years it has been covered by a wide array of artists. Pennywise, Everclear, Weezer, Jimmy Buffett, The Black Sorrows, Creedence Clearwater Revival, Reel Big Fish, Bruce Springsteen, James Taylor, Lagwagon, Steel Pulse, Phish, and The Radiators have all put their own touches on the song.
Personally, I find that none of these covers come close to the original, but they're certainly worth a listen.