If they have a sense of humor...... a few bars of "Release Me".

Van Morisson's "Have I told you Lately" is awesome. I like the arrangement especially the string/piano in the beginning.

Great for slow dancing for sure.

In addition to the songs already listed, I try to play the song that the anniversary couple selected for their offiical opening bride & groom dance at their wedding reception. These typically (but not necessarily) include the popular romantic ballad at the time (year) they were married or engaged. - Scott

Look At Us
When Your Old Wedding Ring Was New
Anniversary Waltz
Unchained Melody

Gary

Great suggestions guys. I already know many of these songs, but I forget about using them sometimes. I'm making a list of good anniversary songs now.
I actually HAVE played Please Release Me at anniversary parties, in the proper spirit of course!
Thanks guys,
DonM