Writing and performing your own songs is great fun - you can fluff the words and/or tune and nobody's any the wiser. It's only when they take on a life of their own and people start singing them back to you that I'll start worrying. I'll get back to you on that one.
Therefore I'm a bit picky when it comes to covering other people's stuff: I avoid popular songs like the plague: the one cover on my Pickering Place EP is a very obscure Slade B-Side which even the writer Jim Lea would struggle to recognise as one of his.
But when I play Tom Petty's Walls, I don't change it at all. And the last time I saw Wreckless Eric and Amy Rigby they played it with a straight bat too. It's just such a good song. Who couldn't be moved by the last verse:
Some things are over
Some things go on
Part of me you carry
And part of me is gone