In rock, most bands play their own material. There are "tribute" bands who play another band's material, and occasionally bands will play "old standards" to fill out an album, but it's fairly rare for rock bands to play covers.
In jazz, there are "jazz standards" that everybody covers, but a lot of players write new tunes and the ratio of old-to-new is maybe close to 50/50 (depending on the band).
In the blues, old songs and new songs mix in ratios similar to jazz, again depending on who you're talking about.
But in classical music, unless you're talking contemporary classical, everything is "covers" -- although you never hear that term in classical circles.
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