After trying them out in the past, I only use SHIVs in endgame now. This is because
(a) Hover SHIVs are available
(b) By this point in the game, money is no longer tight (Although Elerium may be, and SHIVs require that too)
(c) Hopefully I'm no longer too desperate for promotions....

Hover SHIVs with plasma weaponry have 20 health, 40 defence, something like 95 aim, a gun that seems to be equivalent to a Heavy Plasma, and the ability to fly - with twice as much flight fuel as Archangel Armour. They can also move a really long way in one turn. The high defence is to some extent cancelled out by the fact that they can't use cover, but they still make for very mobile, very accurate and fairly hard-to-kill units. On open maps I sometimes use them as flying scouts.

They're certainly not a good substitute for a soldier in all circumstances, but Plasma Hover SHIVs can be a good choice in some circumstances. I'm not at all convinced about the lesser varieties, in terms of their abilities or the cost of developing them earlier in the game.