IMHO if you want to make it memorable, either choose something that is completely out of your normal style and rework it to what fits your music (and Britney Spear's "Hit Me Baby One More Time" has been done before

) or play something that is soooo left of centre that people'll be speechless.
My band is a rockabilly-band but our singer used to be a rapper (

) so at some shows we do the Beastie Boys' "Intergalactic" with the two-note intro to Queen's "Under Pressure" and a 4/4 drum beat to supplement. No guitars. People absolutely love it, but it was supposed to be a one-off and now they want it every show.