Gershwin's "Summertime" has just become my show-off tune. It's not especially hard, but it works well with my voice and shows off my low range. Also, I enjoy singing it, and it shows.
A good friend of mine plays guitar, and we'll occasionally do Kansas' "Dust in the Wind" to show off the fact that we can sing harmony together. Again, it's a case of really liking to sing it...that shows, and it makes the song more enjoyable for the audience, I think.