It may have not been a summon under the players control exactly but as for one I'd like to see again it would have to be Ultimecias Griever from FFVIII. I always enjoyed fighting him and thought it was a pretty cool concept. Aside from Griever I'd have to agree with all the classic summon suggestions on here. Either a primal or an avatar in a summoners hands I'd just like to see these in FFXIV.

Another generally forgotten one would have be FFVIIIs Eden, if that would ever be put into another game (like FFXIV) I'd imagine that would certainly be a primal only, that thing was massive...