So, I've seen a number of simple physics mechanics used in fairly interesting games, recently. Both before and after Angry Birds - I don't know that Angry Birds really changed how common that mechanic is.
Most of them use some form of gravity + bounce - for example, the dozen
or so pirate games where you shoot your cannon, or the million or so
"fire as far as you can" games. But don't let that fool you into thinking they are the same kind of game as one another - I'll get to that in a minute.
I've also seen a few gravity-less throw-and-bounce things, which work out similar to billiards, except usually with stats and hit points.
Fundamentally, these games are all about taking your best shot and seeing how well it goes. Well, with the exception of certain pirateship games, where once you understand the arc you just spam the angle of attack and don't worry too much about the particularrrrrs of what ye be hittin'.
The "fire as far as you can" games usually feature no real skill or tactical decision. Some do allow you to affect the flight of the projectile after you release it (jet packs, shoot it, etc), but the level moves by much too fast for the player to register the situation he's in, so they boil down to heuristics and can be considered to have "optimal" solutions, at least for the limits of the player's reaction speed. I consider them like a slot machine where you have the ability to shout "NO" and pound the machine to get it to spin one more time. Which, you know, doesn't make the result any less random, but at least you get two plays for one coin.
I'm not a fan of the "fire as far as you can" games. Instead, I prefer the two other subsets I can think of: the "combo" games and the "accuracy" games.
Combo games usually feature no real control over your initial strike, but you are allowed to build the room in which the projectile(s) bounces. This makes it a fun, if extremely easily solved and short-lived, tactical base-building challenge. I also like combo games because of the long length of time that the projectile remains in flight, but simultaneously remains affected by your choices (of how to lay out the room).
Accuracy games, like Angry Birds, lie on an axis running from "the cascade" to "the pinpoint". Angry Birds is quite far on the pinpoint side of things: there are specific "best shots" and they frequently have specific results. The birds rarely do a whole lot of damage after the initial bounce, unless you've carefully aimed it so that the initial bounce wasn't the point and it's the next impact that matters.
On the other hand, most of the pirateship games steer more towards cascade, where any given good shot will generally hit several targets - several sails, or bouncing from cannons into the deckhand and then up into the sails, or whatever. This complexity means that, while there is still probably an ideal shot, it's not humanly feasible to find it and instead you should fire in at an angle that seems likely to hit all the things you want to damage.
Of course, things aren't cemented into their role - Angry Birds does have some cascade moments, and the pirateship games may have some moments where you really want to hit a particular tiny part of the enemy ship. Also, some games fall midway between the two, such as most of the billiards-style games with no gravity, where you can often wrangle the rebound into something useful, or at least have to worry about the rebound turning out disastrous.
Most of the games are against stationary enemies, and your real enemy is either the timer, limited shots, or both. Some have enemies which fire back, but they usually serve as a complicated timer, where you can knock off the front rank to buy a little more time.
I've been thinking about new styles of gameplay you might be able to pull out of this system. This has led me to think about the core draw.
I think the core draw of the gameplay is watching your play pan out. You make a shot, and then you just watch it. You watch your calculations and instincts play out. That's certainly what I like about those games, and why I'm not a fan of the "fire as far as you can" style games.
Watching your shot play out has a little more depth than you might think. There's nothing wrong with the fast, highly repetitive loop of something like Angry Birds, where you replay the same level eight times before you get the shots just right. There's nothing wrong with the cascade style, either, where the results of each shot have a more complex and interesting result that takes longer to see.
Personally, I think there are two things that are often overlooked which could make an interesting game in this style.
One is level setup. Letting the player affect the level and then feeling great when his shot is accelerated by his booster or feeling irritated when it speeds on by. You would either need to have all the gameplay take place in the same confined map (so the player can hone his placement) or you would need to come up with some clever and interesting way for the player to quickly and meaningfully place level mods.
The other is disastrous rebounds. I really like the idea that a particularly bad shot doesn't just miss: it bounces back and hits you! You need to be careful!
I was thinking about what you could do with level setup and disastrous rebounds, and here's what I came up with:
Witches' Academy. The witches do battle by lobbing magic balls of energy at each other just like any other game. However, you're not going to hit your enemy directly. They are too far away and there is a shield above and in front of them.
When your shot hits the ground, it summons a spirit or monster, which marches in the direction it was going. If it reaches the magical energy pillar of a witch, it tears it down a notch (and then the pillar creates a shockwave that destroys all spirits).
The spirit your energy ball summons depends on how many times it has bounced.
So, if you summon a zombie with your level one spell, you can then bounce your next shot off your zombie's head, killing it, and when that shot lands it'll summon a skeleton. If you bounce your spell off your skeleton's head, it dies and your shot still just produces a skeleton. You need to bounce a lot, but there's no advantage to destroying your own high-level units to do so.
Of course, your enemy's units are also around to get destroyed and give your magic bounces. And it doesn't always work out ideally: if your magic ball is actually bounced back in your direction, your spirit will be summoned coming at you, not the enemy! Or, if you're clever, you could fire it such that it never lands, but bounces up from beneath the protective shield and hits the enemy witch directly.
The game is made more complicated by having somewhat complex interactions between the units, the levels, and the magic spells. For example, that witch's spells are all paper dolls. They don't bounce magic back up, so you can't use them to bounce! And neither can she! That giant crawling spiny centipede can take multiple hits and usually "captures" the shot, so it bounces against the spines several times and gives you a really strong creature! Which, knowing your luck, will be coming at you, not at the enemy.
This level has pits, or lava, or spikes, or traps that move on a timer, or a mechanism which pulls the witches steadily closer to each other... These spirits fly rather than crawl, these kick other spirits down, stunning them, etc, etc.
Another element I liked, but that isn't compatible with that game design, is the idea that you start at a given range from your enemy and it changes. You have to shoot them down before they escape, or before they get close enough to shoot you back. This has been done in a few games, and it's kind of interesting. I think an airship game using that mechanic could be quite fun, although I'm not entirely sure what the best specific design would be. Maybe a ball-on-a-long-chain mechanic, where you can reel the shot in after you fire it to recover it from the sky below you or drag a caught ship closer...