I think I recognize most of the songs, so let's see.
1. Like Someone In Love -- probably a foxtrot if it's the song I'm thinking of. If it's slow enough though, you might be able to do rumba, but I don't think the song has a rumba feel to it.
2. I've Never Been In Love -- I don't think I know this song.
3. As Time Goes By -- should be foxtrot
4. Change Partners -- foxtrot; the HCJ version gets played at dances I go to now and then
5. The Summer Wind -- should be foxtrot
6. Something Stupid -- I think dar is right, probably rumba and if it's on the quick side, American rumba specifically
7. If You're Not the One -- I don't think I know this song either
The same song can be played in different ways leading to different dances that best fit each given version. But Frank Sinatra stuff is often foxtrot and anything with a similar sound, feel, tempo, etc. ought to be foxtrot as well. Something else you could try, rather than asking here where people may know the song but not by the same artist you're asking about, play the songs for some dance friends you know. They'd be able to tell you pretty quickly from just hearing a little bit of the music what dance would best fit the song. I hope this helps.
--
James Marshall
marshall@astro.umd.edu http://www.astro.umd.edu/~marshall 
