I've always been a Smiths guy, but a lifetime of them and nothing but them alone on an island would drive me to engineer a potato gun and just end it all, which might be for the best. R.E.M. would be a contender, but everything after "Document" basically sucks so that would render more than half of their catalogue useless. Pavement is right up there.
But if I can have one and only one, I'm going with The Replacements.
REM was up there for me, too, but definitely earlier stuff. They have longevity, but I don't really need all of the sadsack stuff.