I'm gonna throw my thoughts in then read n respond to others.
My first game with a morality meter was probably Mass Effect. I think. There may of been something with a more hidden off moral meter that I can't remember at this moment in time.
As for likes n dislikes, I'm pretty vocal on my dislike of the Mass Effect style "save the kitten" vs "burn down the orphanage" style. Even worse when it's Up for Good Down for Bad. It's so simple. It's just a "pick which stat you want to charge up" mechanic than actually getting you to think on your choices and potential consequences. Before ME2 launch my housemate managed to complete ME1 in about 8hrs or so, with a fair chunk of time saving in skipping through convos then pushing up when the wheel popped up.
I liked DA:O's style, it was along the right tracks. It's style and timing suggests that Bioware had eyed up another game I'm fond of, which would be Witcher. Witcher had none of this up=good, down=bad choices. And very rarely any kind of obvious good or bad answers. Many shades of grey. And sometimes the choices with consequences weren't necessarily moral choices*. Just questioning a dwarf about the scoia'tael will piss him off and he won't trade with you. Actually wait no. One won't talk to you. If you kill a particular elf or piss it off, then a different dwarf won't trade with you. It's a game that makes you pay attention to what you're talking about, what convo options you're picking. (whereas Mass Effect/DA2 you push up or down and the result is the same)
Infamous had a painfully black n white system. But what I did like about it was that it changed the game. Depending on the path you pick depends upon which powers you got and could change your play style quite a bit. (good was more defensive, evil was offensive). So in a story sense it was pretty bad, as a gameplay mechanic it was pretty enjoyable and gave you at least two playthroughs out of the game.
Oh yeah Postal 2 was pretty fun with it's stuff. It was more making a point than anything I guess, but it was designed so you could go through the game like a regular guy, buy your milk, take books to the library, cash cheques etc. But you can do them the slow n dull way, or pull out a gun n shoot the place up. Or piss on it. upto you. The game doesn't force you too much one way or another. (It's not totally balanced, so does push you a bit to the shooting part)
Not that I can remember off the top of my head. Loosing access to the dwarf blacksmith was pretty annoying, but it was my own fault and I did kinda like I was punished for been a lazy gamer at the time.
I think FPS games could work with it. But they'd need a bit of a revamp first. GTA or similar would be an obvious one. LA Noire I could see fitting a morality meter or sorts, depending on how you go about your ways. right n proper, or corrupt, maybe a little over the line in getting evidence and confessions etc.
I'd improve it by getting rid of it. Don't have some stat on the menu with a bar going up or down. I'd go with the Witcher shades of grey style. No more black n white choices. DA:O was going so well and then..DA2 happened. *I also think maybe the prefix of 'moral' should be taken off, and just be games with 'choices'. Maybe a suffix of 'and consequences'. That's all it should be. How many times in a day do you have to make "moral choices" compared to just regular choices like if you're gonna write that essay today, with the consequences of completing it peace of mind n good grade, or staying up all night n probably missing hand-in. Do you go to the shop and at the till have to decide everytime if you're going to buy the milk, or stick a gun in the guys face n rob the store? It's not very natural. And if you have these stark black n white options then it creates an inconsistency if you go with the good ones most of the game, then suddenly go for a streak of evil choices.
I think that final paragraph would be my main point. Shades of grey, less "moral choices", more cause n effect.
@Kenshi: Ah I'm not the only one in camp "hide the meter". Also I found Evil to be pretty sucky cos the good side had the ability to let attacks charge up your power through the shield. I've yet to get to the final boss fight, but it'll be a bitch without being able to stand n shield against his attacks to charge up.
@Hot heart: See RDR felt like it was tacked on. It meant nothing, and it totally clashed with the story "I'm a reformed man" "I don't do that kind of thing no more" as you're dragging a hooker behind your horse on a rope.
@Johhny: I have heard good things on Vampire The Masquerade. Supposedly has one of the better VG stories out there (though with dipping a bit at the end) I may look into it over summer. (GOG have one up btw http://www.gog.com/en/gamecard/vampire_the_masquerade_redemption )
@Pirandello(sort of) NWN had a moral choice thing? I can't remember as such. But if so that's the first game I've played with a moral meter then. Didn't get too far or remember much of it though.
@Thursday: Pretty spot on.