Hi,
I sing; in fact, my voice is my principal instrument (I'm learning the DB to fulfil a long-time dream).
Your choice of mic will very much depend on your voice, I'm afraid. As with basses, there's no substitute for going to a well-stocked music store & A-B'ing some side by side. Some flatter well for some people whilst sounding terrible for others (male vs female voices is the obvious case, but differences in tone, timbre & range between voices within the same gender will still apply).
To give you an idea of what I use, though; I'm a baritone in range & a jazz vocalist. Being a vocalist, tone & refinement is paramount for me in a mic. I can cover from about a G2 to G4 (middle G) and currently use a Heil PR35. Really, really, really nice dynamic that's quite unlike most; plenty of midrange & top end and not muddy at all. Massive diaphragm, & the closest I've heard a dynamic get to a condenser. Speaking of which, have a listen to my tracks on my website:
www.swingingoodtime.com/music.html These were recorded using a Shure Beta 87a. The beta 58a (dynamic) is pretty good, but I find it a bit harsh compared to the Heil or the 87A for my taste.
Alternatively, ribbons can be quite nice; very smooth & forgiving with a lot of voices. One of the cheaper Chinese types could be a go-er due to affordability and that the ribbon appears to be more robust than usual; (ironically, use of cheaper (thicker) materials for the ribbon appears to be a slight advantage, albeit at some expense of hi-end response). I used one of these for a while & once accidentally put 48V+ across it for about 10 secs with no problems. I also re-housed mine in a Shure 55SH 'birdcage' replica housing which sounded reasonably good (I also swapped out the std transformer for a Lundahl), but the housing introduced some resonances that caused occasional feedback problems in a live setting, so I've retired that for now until I can fix the problem.
You can hear the different mics in action on my videos page (
http://www.swingingoodtime.com/videos.html . Set 1 is the Beta 87a, Sets 2, 3, 4 & 6 are the ribbon and Tracks 7 & 8 are the Heil. 6 & 8 are particularly good for hearing the mics, as I was able to multitrack rather than just record a stereo ambient track.
I also tested found the EV N/D767a (dyn) to be pretty good and surprisingly affordable, as is the Sennheiser e935 (dyn); not my first picks, but adequate. The Sennheiser e945 (dyn) & e865 (condenser) are both really, really nice but up there in price. I could have gone either of the first two but was fortunate to pick up the Heil second hand instead. The e845 (dyn) i sok, but not particularly special. Haven't tried the new e965 (cond).
I didn't like the AKG D5 as it was too bright, a bit harsh & not very warm sounding for my voice; I like a sound which has a creamy, smooth low-end but with sufficient mids to avoid sounding muddy & thick.
SM58 (dyn); yuck. Great rock mic, but yuk; muddy as. Re comments: "[xxxxx] sounded better than an SM58"; heck, they're designed for withstanding physical & vocal (screaming) abuse on rock tours, not for refined audio-reflection. So in a jazz context a great number of mics will probably sound better (although I heard a female voice folk/bluegrass recording once that sounded good; the muddiness gave her voice lower end presence & took the shrillness off the top).
Other mics:
Rode M1 (dyn); better than the SM58, but still not very refined (it's touted for rock, not jazz!). Rode S1 (cond); to much high-end, no creamy bottom end. Haven't tried the S2 or M2 (both cond). Shure 87C (cond, but NOT a Beta model, btw); not bad, but the 87A had the edge for me; a little more refined, although not much in it. the 87C seemed to have a little more bass bloom, which sounded like it would be good for a female voice (balance out shrillness). Haven't tried a Neumann, but then I'd never take something that expensive to a gig.
Overall, like basses, if you do a lot of singing; spend some bucks on a decent mic. You won't regret it and nor will your audience as, providing you're trying to sing well, a good sound will give you confidence to sing even better.
To re-iterate; these opinions apply for my voice, to my ears, and supported through positive feedback of listeners. At the end of the day, there's no such thing as a mic that can't be used somewhere; the SM58/female vocal example cited above is a perfect example.
Hope that helps!
