Most dry meads can be carbonated with little problem if they are not too high in %ABV. With sweet meads, you almost have to force carbonate with CO2 (in a keg or other pressure vessel).
The reason for this is the yeast. In a dry mead, your little yeast beasties have consumed all of the residual sugars available. When fermentation is complete, you can add a specific amount of sugar to produce a specific amount of carbonation just like you would for beer. You sometimes have to add more yeast but they can still only eat the amount of sugar that you have added.
A sweet mead, however, still has plenty of residual sugars available. Either because the alcohol level is higher than the yeast can tolerate and they've died off or because you have stopped the fermentation with sulfite and sorbate. If you add another yeast with a higher alcohol tolerance to produce carbonation, they will keep eating until they, too, reach their tolerance. It's not something that is as easy to control as it is with a dry mead. It can lead to bottle bombs: limb shredding, dermal abrasion, lacerations and eye gouging as well! That's why force-carbonation is your best bet for sweet meads.
As far as styles that lend themselves to carbonation: I've sparkled a few ciders and cysers in the past that were nice and refreshing when served ice cold on a summer's day. I would imagine that any light flavored mead would work well for this. Kind of like a chamagne, if you will.
One more issue. If you are going for a still mead, be sure to thoroughly de-gas it by gently swirling for several minutes before bottling. I once had a currant/strawberry mel that I thought was still but ended up being slightly carbonated just from the residual CO2 in the must. The bite from the carbonic acid hit at exactly the same point where the currants and strawberries combined and really wrecked the flavor. If I swirl it in the glass for about 15 minutes, it's fine. That first sip after a pour, however, is
!
Hope this helps!
Wade