Classic:
SHoDANAUT - Short Hop DAir NAir UTilt, the old and still pretty good damage building combo. The faster they fall, the more uTilts you should do. Then uSmash or uAir to continue the combo if you can.
Hyphen Smash - Dashing uSmash, which is Luigi's replacement for his horrible Dash Attack. Follow up Fireballs with it once in a while.
Lagless Shorthop Double-Aerials - You can basically string together two of the following aerials: fAir, dAir, and uAir, in any order (with the exception of udAir) and have 0 aerial landlag. You can also end any Shorthop Double-Aerial with nAir and have very little aerial landlag. With all those different combinations of double-aerials you can cram damage and still be quick on your feet.
FAir to GM Momentum Canceling - When you get launched by an attack, fAir will help you regain control quicker. Then, if you're being launched sidways, uncharged GM toward the stage to quickly cancel Luigi's horizontal momentum. Combine this with ASDI, SDI, and DI, and you've got yourself a very survivable Luigi.
B-Reverse - Just in case you aren't doing it already. Very handy with the Fireball.
Jab Cancel - Just do it a lot. A lot a lot. Mix the Jab Cancel followups. Jab Grab too.
RAR - Reverse Aerial Rush, all over their faces.
Delayed Recovery - Wait longer than normal to try to get back on stage when knocked off, it throws off the timing of the opponent and allows you to punish them if they chase you. Two ways of doing this...
From the Side: tilt the analog AWAY from the stage, allowing you to avoid Marth's and MK's fAir WoP
From Below: fall farther down before using your Rising Cyclone to get back, which helps make the opponent mistime their Meteor Smash and ups your chances of gimping them if they chase.
New-Age:
FFAD - FastFall AirDodging, one of the most important ATs to know. An aerial attack, then invincibility, then only 1/15th of a second of landlag.
JRC - Jumpless Rising Cyclone, another of one of the most important ATs to know. S*** man, if you are ever doing your regular Rising Cyclone and the opponent hits you away, the only way you're getting back is knowing how to JRC. Turn your finger into a vibrator for the sake of Luigi.
Crawldash - I personally ****ing hate this AT and believe it's just a waste of time/effort, but everyone's doing it and they swear by it.
You can check out the Green Glossary to learn how to do the ATs you don't know about.