Since there are so many Final Smashes, I'm going to make a table of them and how to avoid.
Final Smash | Character | How to avoid |
Mario Finale | Mario | Don't get caught between the fireballs. The fireballs can be dodged but not shielded. |
Konga Beat | Donkey Kong | Stay far enough away from DK's sound waves. Hits timed to the music have a much longer reach, so watch out for them. |
Triforce Slash | Link, Toon Link | Don't let Link/Toon Link hit you with this move's initial beam of light. |
Zero Laser | Samus | Don't get hit by the laser. Can be shielded and dodged; however, this attack's duration makes this ineffective. The suit pieces left behind can be shielded, dodged, and caught like any regular item. |
Power Suit Samus | Zero Suit Samus | Avoid the initial burst of energy, as it will draw you in to Samus. Dodging is possible. |
Cook Kirby | Kirby | Stay far away from Kirby when he bangs the frying pan. The sucking diamater is about the length of Final Destination. |
Landmaster | Fox, Falco, Wolf | Don't ride the Landmaster. Don't get crushed by the Landmaster. Don't get shot by the Landmaster. |
Volt Tackle | Pikachu | Just run. This attack cannot be effectively shielded or dodged. |
Critical Hit | Marth | Avoid Marth's initial rush. It hits through shields and is undodgeable. |
Octopus | Mr. Game & Watch | Stay away from the octopus. You can dodge around it if need be. |
Negative Zone | Luigi | Don't go into the Negative Zone. If caught, leaving is difficult due to the nature of the attack. |
Rocketbarrel Barrage | Diddy Kong | Aside from running, this can be dodged and shielded like any normal attack. |
Light Arrow | Zelda, Sheik | Jump. |
Palutena's Army | Pit | The Centurions can be dodged and shielded. Pit is allowed to move while the Centurions attack, so beware of him in the ensuing chaos. |
Galaxia Darkness | Meta Kight | Don't get hit (or for that matter, don't let anyone else get hit) by Meta Knight's initial cape sweep. The cape breaks through shields and dodges. |
Triple Finish | Pokémon Trainer | Ivysaur's SolarBeam will trap you in the attack. Hydro Pump and Fire Blast can be dodged and shielded, but be careful not to air dodge into SolarBeam. |
Great Aether | Ike | Don't get hit by the initial burst of fire Ike swings from his sword. This fire can be shielded and dodged. |
Grenade Launcher | Snake | Snake's grenades take a moment to reach you from wherever he's firing, so use this delay to run. The grenade explosions can be dodged but not shielded. |
Peach Blossom | Peach | Stay away from Peach when she executes this attack. Remaining airborne appears to prevent sleep. |
Super Dragon | Yoshi | Yoshi's fireballs are undodgeable and unshieldable. Yoshi himself, however, is. |
Beast Ganon | Ganondorf | Beast Ganon's initial roar will paralyze you if close enough. Undodgeable and unshieldable, but can be avoided by jumping above him. |
Iceberg | Ice Climbers | Avoid the coldness raidiating off the iceberg. Standing on it too long can freeze you. |
Waddle Dee Army | King Dedede | Avoid the Waddle Dees, Waddle Doos, and Gordos. Jumping is good, since they run very quickly on land. |
Aura Storm | Lucario | This move cannot be shielded and is difficult to dodge through due to its size and entrapping power. Stay to the left or right of the beam. |
PK Starstorm | Ness, Lucas | Each star can be dodged but not shielded. Be careful not to doge into another star. |
Super Sonic | Sonic | Super Sonic can be dodged but not shielded. Pray that the person using him has a hard time controlling this Final Smash. |
Giga Bowser Transformation | Bowser | Giga Bowser can be dodged, shielded, and reflected just like in Melee. Good luck avoiding him. |
Wario-Man | Wario | Just like with Giga Bowser, Wario-Man's attacks can be shielded and dodged. Unlike Giga Bowser, Wario-Man didn't appear in Melee. |
Diffusion Beam | R.O.B. | The Diffusion Beam is unreflectable and unshieldable, but can be dodged. Take care when didging since the beam will trap you. |
End of Day | Olimar | Olimar's ship can be avoided by dodging. Escape from the Bulborbs is possible by jumping high enough, though this is only really possible for characters with multiple midair jumps. |
Blue Falcon | Captain Falcon | The Blue Falcon can be dodged when Captain Falcon tries to hit you with it. Even though it swings out slightly in front of him, you can't avoid it by standing directly next to him. |
Puff Up | Jigglypuff | Try to stay away from Jigglypuff (she'll make this easy for you). Don't touch her, however, when she yells at the end of this attack. |
I wrote and tested this all myself, so tell me any mistakes you may find. It took me three hours.