Okay, so I give credit to Lord Golbez for suggesting the idea on character discussion threads for Brawl. I'm making this thread on Luigi and a guide to using him. Let's begin, shall we? ;D
First, let's review Luigi's moveset. That's the first thing you should know.
A: Punch right, punch left, butt smack (lol)
Side A: A hand jab
Up A: Luigi throws his fist in an arch above his head
Down A: Luigi swings his feet in a circle around him for a kick
Up tilt: Looks a bit like up A, but the arch isn't as big
Down tilt: Luigi kicks behind him
Side tilt: Luigi kicks
Running A: Luigi just punches wildly in front of him
Neutral Aerial: Luigi kicks while airborne
Up Aerial: Luigi flips and kicks upwards
Side Aerial: Luigi karate chops
Back Aerial: Luigi kicks with both feet in a horizontal line behind him
Down Aerial: Luigi kicks with both feet vertically downwards
Grab: Headbutt
Up Throw: Luigi takes his opponent and throws him/her up in the air
Side Throw: Luigi takes his opponent by the feet, spins a couple times and throws them
Down: He just shoves them to the ground
Standard B: Green Fireball
Side B: Green Missile
Up B: Super/Fire Jump Punch
Down B: Luigi Cyclone
Final Smash: Negative Zone
Now the key to Luigi is to make use of his aerials as much as you can. He can use them several times in one jump, which can easily rack up damage. While on the ground, the fireballs will be helpful, especially against those characters who don't have projectiles. Luigi's running A is good because it has some knock back and the distance the last strike hits the opponent gives Luigi a lot of space for a fireball + Green Missile combo.
However, miss with running A and Luigi becomes vulnerable. You should only use it when a character is charging an attack in front of you or to do some edge guarding. Now, moving on to his other A moves, Luigi's hand jab is easily the strongest of his A smashes. Makes good KOs, if you can dodge and then strike when the opponent is high damage. It comes out fast, and if you can time it right, charge it up and it has the potential to KO an opponent that is under 100% damage.
Luigi's down A, however, has the most range, and therefore it's good against other characters with good range when you can get in there fast enough. It's especially good against the slow powerhouses, such as Ike. The same can be said for Luigi's back aerial, only it's done while airborne. Luigi's down aerial is a good meteor smash, however it's a bit tricky to pull off because it sometimes won't push the opponent straight down. You've got to aim it just right in order to make it work like a meteor smash. Another good tip: use hand jab or karate chop RIGHT AFTER using fireballs. While Luigi's hand is still flaming, it makes the two moves deal a bit of extra damage.
Up A and up tilt, however, are only good for running in and striking before a slower opponent can hit Luigi. Then combo it with up aerial and side aerial via short hopping if you can. The short hopping allows Luigi to pull off these moves a little faster than usual. Fast falling can help with a meteor smash, but is effective over the stage as well, especially if you've missed with Super/Fire Jump Punch.
And speaking of Luigi's B moves, remember what I said about fireballs being useful on the ground. They're your friend. Fire Jump Punch is what you should be pulling off instead of Super Jump Punch because SJP does only 1% damage. Fire Jump Punch is powerful enough to make a KO below 100% damage. However, like running A, if it misses, Luigi becomes vulnerable. It's best used against slow characters with moves that lag and make them vulnerable, or when any character misses a laggy move.
Luigi Cyclone is good for racking up damage and sweeping across the stage by moving Luigi side to side. This way he can hit multiple opponents at once. It can also serve as a recover move much like Super Jump Punch. Only here, repeatedly press the B button to make Luigi rise while performing the move. Green Missile is a VERY good recovery move and is easily the most ranged non-projectile move in the game. Luigi goes even farther than normal on a misfire, which I'll be covering in a moment.
Green Missile, most people say you shouldn't use it because it's a bit slow, laggy and hard to hit with. This isn't true. Green Missile is actually a very good move to use and timing it right isn't all that difficult if you put your mind to it. It's also effective in the Green Missile/fireball combo where Luigi shoots fireballs and uses Green Missile alternatively. Misfires are extremely powerful, but only happen by chance. That's why your aim must be timed right, because who knows, you may get a misfire and KO the opponent. ;D
To get around the move's slowness, trick your opponent by charging and waiting for a good moment. Of course, while charging, an opponent can attack you, so only do this do characters who don't have projectiles and when they're at a good distance. Another way is by attacking close up in the air or on the ground, though it's easier in the air. I've managed many KOs with misfires doing this.
Now we move on to throwing. Luigi's side throw is most powerful and effective, though the up and down throws are good for combos. Use the combos when your opponent is low damage to rack up some damage, and use the side throw when the opponent becomes vulnerable and gets high damage. It's very likely to be a KO.
Lastly, Luigi's
FS. When you've got smash balls on, Negative Zone can easily help you turn around a tide. It can do all sorts of stuff to opponents and make them vulnerable to anything, so use hand jab or Fire Jump Punch (preferably Fire Jump Punch when their damage is below 55%). To make your opponents get caught in it, use it near the edge of a stage and get as close to the opponents as possible. The closer they are to Luigi, the farther from the edge of the Negative Zone they'll be, and as a result it'll be harder to escape before any of the effects stop them.
I believe that covers pretty much everything. Want me to add something? Just ask. :]
Now for Luigi's difficult character match ups. Here are some tips for a few.
Ike: Yeesh, is this guy a pain. I'd hate to do this to my favorite swordsman, but it must be done when I use Luigi. But anyway, Ike has two big advantages over Luigi: range and power. A good Ike player can time his slow moves right and pummel the guy. For a match like this, fireballs and Fire Jump Punch are your friends. When you dodge Ike's slow moves, he's vulnerable, so get in there and Fire Jump Punch him. Ike players are likely to use Aether, Quick Draw, and Eruption a lot, so pay attention to when he uses them. Aether can easily be dodged by moving side ways out of the way because it goes straight down. Eruption is a bit laggy and causes Ike to be vulnerable, so Fire Jump Punch is your answer. Counter Quick Draw via fireballs to stop the mercenary in his path. Also, be careful when Ike uses Counter. You shouldn't attempt to meteor smash him or Marth because of this.
Marth: Yeah, Marth can be a pain too because of his speed and range. Luckily, he doesn't have the power that Ike does. Anyway, blocking is essential for Marth's better speed, so do it often (just not too often or it'll break). Fire Jump Punch is a no no unless Marth uses Dolphin Slash or Shield Breaker. They lag a little bit. And speaking of Shield Breaker, don't block for this, dodge it. That's why it's called Shield Breaker. Fire balls are your friends here as well because Marth can't attack from a distance. Block for those A moves, though, they're quite fast. Counter back with A moves of your own and a fireball/Green Missile combo if you'd like, or use the A smashes after fireballs. And as with Ike, be careful when Marth uses Counter.
Link: Ugh, this guy's projectiles can be so annoying sometimes. In order to evade them, DON'T use Green Missile. Instead, block or dodge, and shoot fireballs. Meteor smashing will be useful here because Link's recovery isn't exactly the best. So make use of that down A! Fire Jump Punch should only be used when Link misses you with a Spin Attack. Green Missile works in the air, but only when Link doesn't use projectiles. Luigi's hand jab will be useful for KOs because it's both strong and fast, and Link isn't a heavy character. Use it on him before he can hit you, and dodge his strike if necessary. That's it for this guy right now, will update when I find other good techniques against him.
Meta Knight: Pretty much any character will have some kind of trouble against Meta Knight due to the fact that he's like...at the top of the tier list. Luckily for Luigi, Meta Knight has a few moves that will make him vulnerable and easy to land a Fire Jump Punch on if he misses. Two of them are the tornado move and side B. Meta Knight's moves also come out quickly, so block. You can stop his side B using fireballs as well, though it's a bit tough because that move is fast and unpredictable. Also, dodge often as well as block. I don't know much more about Meta Knight, will edit this section.
Snake: Now here's a guy who is quite troublesome as well. Remember that Snake has more projectiles than any other character in the game. He's likely to try shooting his straight up at you when Luigi is airborne above him, so be careful and keep using that dodge button. On the ground, get Snake to miss with his projectiles and Fire Jump Punch him. Green Missile will also work. Make use of Luigi's aerials as much as you can when Snake is up in the air as well and god dammit, don't fall for his stupid mine trick. Watch closely where he puts those annoying things, got it?