Dusty Springfield - Son of a preacher man.
Killing me softly - 2 versions of this the fugees covered it not sure who done the original,
Lot's of others...

Depends on what sort of genre of song you are looking at aswell I suppose...

Singers like Kylie or Madonna could be described as having voices that aren't really quiet but equally aren't hugely powerful, so their songs could work. Or some of Dion Warwick's Burt Bacharach songs - Walk on By or Say A Little Prayer, for instance.

Most girl-band and boy-band songs are fairly neutral in their content - realistically, groups do not tend to have one 'belter' and then lots of backing singers these days, they are all pretty middle-of-the-road voices, when you compare them to the great divas like Mariah, Whitney, Celine and Carole (Decker).

Songs by ex-band members would be good - any of the Emma Bunton songs, for example.

If you are thinking of songs that the peculiar blonde girl on X-Factor could sing (Diana Vickers), her particular style means that she can probably take on most songs, but just sing them in her own unique (read: nasal) way, and get praise even though she sounds like she is playing a kazoo at times. Disco week will be quite interesting - far less scope for her particular portamento between notes, although with a bit of luck, she'll pick something upbeat and lively that will see her kicked off this week!