A Strong Down, also known as a Down tilt (abbreviated "d-tilt,") is a Strong Attack performed by any character by holding the control stick lightly down or crouching and pressing A while on the ground. It will instantly hit all surrounding characters, making it useful for spacing. It is also useful for a foe rolling around you. It can also be performed by pressing Z while crouching.
Pikachu: A moderately high knockback move with surprising range (similar to most of Pikachu's moves in this way). Less comboable that Pikachu's other moves. Semi-spike.
Ness: Very quick with low damage. Usually used into a throw or against a wall for a shield break. Can be Smash DI'd out of to prevent a grab after.
Yoshi: Another set knockback tilt (the other one being up tilt) with good power, can infinite against a wall, usually used for gimps. Very good for edgeguarding Fox, Jigglypuff and Kirby. High power semi-spike by the ledge.
Captain Falcon: A good move that has IASA frames. Usually used as a shield stunner in order to throw after. Good knockback. Essentially Yoshi's up tilt but without set knockback, slightly less range, and more comboabiltiy.
Donkey Kong: One of the few low lag DK moves. Essentially a weaker version of Falcon's. Very useful at close range to lead to a grab or down b.
Mario: A low knockback move with a good amount of damage. A sweeping kick. Not overly useful due to poor range and poor combo ability.
Luigi: Similar to Mario but with slightly less range, slightly less lag, and slightly less knockback. Combos into Up B.
Jigglypuff: Similar to Pikachu but slightly less versatile, quicker, and has less range. Good combo ability and works great into rest. A staple Jigglypuff combo is down air, Up tilt x 3 (or more varying on character) and then a Rest.
Samus: A longer range version of Mario. Good knockback and a good spacing move.
Link: A different form of down tilt. Sends an opponent up. Combos into up B and other moves. Too high lag to be used often though.
Fox: Similar to Link's but with more range and slightly more comboability. If there wasn't Smash DI in this game, then this move leads into an infinite with Down air after.
Kirby: A moderate range move that is quite good at gimping and breaking shields.
R.O.B.: Shoots arms very quickly diagonally down at ground. No lag at all, can be spammed, and causes prat falls. edgeguarding spammable. Not much knockback, but good damage racker. Can infinite against walls.
Kirby: Kicks foot forward. Weak, but has a high chance of forcing a trip.
Meta Knight: Pokes sword forward. Similar to Marth's, although faster, and moves him forward a bit.
King Dedede: While crouching, swings foot forward. Ending lag, but strong attack.
Olimar: Pushes forward along the ground. (Comedically, if Pikmin are behind him, it looks like his Pikmin shoved him on the ground.)
Fox: Swings his tail along the ground. Low priority.
Falco: Same as Fox's, but much more priority due to upwards knockback for setting up a spike combo for edgeguarding. Less range than Fox's, but good for combo setups.
Wolf: Kicks out with his foot, having decent range and can cause tripping.
Charizard: Reaches out and bites along the ground. Strongest at the tip of the move where his mouth is biting, weaker at his neck area.
Lucario: Pokes foot out and holds arms behind him. Very similar in appearance to Ness'. Aura imbued.
Jigglypuff: Jams foot forward and low. Low knockback.
Marth: Stabs sword forward. Same as Meta Knight's. Slower than Meta Knight's, but still moves Marth forward, like Meta Knight.
Ike: Swings sword heavily horizontally. Extremely powerful ledge spike and always spike aerial opponents very powerfully.
Ness: Is an infinite foot-jabbing combo in SSBM. In SSBB, it causes prat falls. Good hitstun, but less knockback. Like Lucario's in appearance. This move is great setup for Ness' Up Smash if the enemy trips. 100% of tripping if sweetspotted.
Lucas; A non PSI-powered leg swivel. Can be indefinitely used like Ness', but is incapable of going as fast, and does not trap the opponent. Has a 100% chance of tripping if sweetspotted.
Mr. Game & Watch: Flips a 3D manhole in front of him. Excellent move with good knockback and priotity. Good for combo setups.
Snake: Spins body around in a circle, very close to the ground. Has KO potential on most characters at 120% and up.