There are no rules on this. When doing covers live, sometimes the audience prefers to hear the song as originally done. There are some songs I hate hearing done any other way. But, it's personal preference, mostly. Some bands make a name for themselves by tweaking tunes and essentially making them their own.
Also, if you're the writer, while it's the greatest form of flattery, it can be quite interesting to hear another band interpret your song. Personally, I've often found it inspiring to hear how another band might change my song. Just instrumentation alone can change the whole feel of a song. Paul McCartney has said, as far as he's concerned, there's no bad cover.