What cards or types of cards are substantially more/less useful in Two-Headed-Giant than in 'normal' Magic?
Any cards that care about any aspect of the game that is likely to increase due to there being more Lands, Cards in Hand, Creatures in Play, Higher Life Totals, turns, attack phases, etc.

The above is just a generalization of course. THG is similar to multiplayer in this respect. Aggro decks don't work as well, and Combo and Control decks get better. Some interesting examples are listed below, but in general you should be looking at cards that count things that there are likely to be more of. Truthfully though, most THG decks are built as two puzzle pieces (unless playing draft/sealed). Cards are specifically chosen to complement the other deck. While generalities are useful, they aren't the whole picture.

Life Totals start at 30, and are shared by both players. Any card that counts Life Totals will behave differently. Some interesting examples are:

Heartless Hidetsugu - Instantly kill all even life teams.

Serra Ascendant - Starts off with +5/+5 bonus.

There will be more lands in play, interesting examples are:

Impending Disaster - Almost sure to trigger, and cheaper than Armageddon.

Limited Resources - Broken for Multiplayer, and bad in THG with decks built to exploit it.

There will be more Hands. Interesting examples are:

Unnerve - 1:4 your opponents isn't bad.