Nobody will play like Ringo. I was joking around with a fellow this weekend who played in a Beatles tribute band. Tasteful grooving player, and he is a lefty playing righty so he should be able to nail Ringo. He gets close to the feel but told me that it's much harder than it looks. http://youtu.be/KG0MA1ZErUk
When playing other people's music, start by trying to capture as much of their vibe as possible. You can learn from everybody''s playing. If you're playing in some sort of show/tribute/someone else's band, try to reproduce that. If you're playing in your own band doing your own thing, start from where you found it and then add yourself. Don't shortcut the way you found it.
About a year ago, I was at a jam and was behind a singer who turned out to want everything to be like a runaway freight train. She started the song in free time and didn't count in, so I played it at standard tempo. A friend who is a much better drummer than I was laughing afterwards and said that I played it "exactly where famous and important producers and arrangers had long ago decided where it should be". In the absence of any other direction, I played it like the record. Everyone else knew where to be with the original tempo and groove (as best as I could manage it).