Since we're about half way through the selection process, I'll go ahead and give an update on the current amount of Nominations Pokemon have and what events they cannot particularly do.
Gen 1
Charizard (3) - While it is capable of swimming it most definitely can't dive.
Blastoise (2) - Can't fly
Pidgeot (3) - Can't swim
Pikachu (1) - Can't fly, can't dive
Nidoking (3) - Can't fly, can't dive
Ninetails (1) - Can't fly, can't dive
JIgglypuff (2) - Can't fly, can't dive
Arcanine (3) - Can't fly, can't dive
Alakazam (2) - Can't fly, can't dive
Machamp (1) - Can't fly, can't dive
Rapidash (3)- Can't fly or dive
Dewgong(1) - Can't run and can't fly
Gengar(3) - Can't sky Battle, Can't dive. (can fly however)
Starmie (1) - Can't fly, can't mountain climb
Gyarados (2) - Can't run or fly, or mountain climb
Vaporeon (1) - Can't fly
Aerodactyl (1) - Can't dive
Dragonite (7) - He can do everything.
5 fliers
Gen 2
Typhlosion (2) - Can't fly or dive
Feraligatr (3) - Can't fly
Furret (1) - Can't fly or dive
Crobat (4) - Can't do anything outside of flying events (has no feet)
Pichu (1) - Can't fly or dive
Azumarill (1) - Can't fly
Wooper (1) - Can't fly....... I'm not sure how it can climb rocks/mountains without arms... so it probably can't.
Espeon (2) - Can't fly or dive
Umbreon (1) - Can't fly or dive
Scizor (2)- Can't dive
Heracross (3) - Can't dive
Ursaring (3) - Can't fly or dive
Scarmory (4) - Can't swim
Houndoom (2) - Can't fly, or dive
Kingdra (1) - Can't do anything outside of water.
Donphan (1) - Can't dive or fly,
Suicune (4) - Can't fly
Tyranitar (4) - Can't Dive or fly.
Lugia (1) - I'm guessing it can use its wings to climb the mountain so it should be able to do everything.
5 fliers
Gen 3
Sceptile (4) - Can't fly, or dive
Blaziken (3) - Can't fly or dive
Mudkip (1) - Can't fly
Swampert (2) - Can't fly
Swellow (2) - Can't swim
Gardevoir (2)- Can't fly, can't dive
Vigoroth (1) - Can't fly or dive
Slaking (2) - Can't fly or dive
Aggron (3) - Can't fly or dive
Manetric (1) - Can't fly or dive
Flygon (2) - Can't dive
Altaria (1) - Can't dive
Milotic (4) - Can't do anything outside of water
Gorebyss (1) - Can't do anything outside of water
Salamence (4) - Can't dive
Metagross (3) - Can't dive, can't sky battle
Latios (2) - Can do everything
Rayquaza (2) - Can't run
6 fliers
Gen 4
Infernape (1) - can't dive or fly
Empoleon (1) - Can't fly
Staraptor (5) - Can't swim
Luxray (3) - Can't fly or dive
Rampardos (2) - Can't fly or dive.
Floatzel (5) - Can't fly
Lopunny (1) - Can't fly or dive
Mismagius (2) - Can't do anything outside of the sky
Garchomp (6) - Can't fly, or dive.
Lucario (6) - Can't fly or dive.
Weavile (1) - Can't fly or dive
Electivire (1) - can't fly or dive
Togekiss (1) - Can't do anything outside of the sky
Gliscor (2) - Can't run, jump or swim.
Gallade (1) - Can't dive or fly
Froslass (1) - Can't dive or fly
Giratina (1) - Changes form depending on event, can do everything.
5 fliers
Gen 5
Victini (2) - can't dive or sky battle
Serperior (1) - Can't dive, or climb or fly.
Samurott (1) - Can't fly
Zebstrtika (3) - Can't dive, climb or fly.
Excadrill (6) - Can't dive or fly.
Conkeldurr (3) - Can't dive or fly
Seismitoad (1) - Can't fly
Leavanny (1) - Can't dive or fly
Maractus (1)- Can't dive or fly
Archeops (3) - can't swim
Zoroak (2) - can't dive or fly
Chandeleur (1) - Can only fly - cannot sky battle.
Haxorus (1) - Can't fly or dive
Beartic (2) - Can't fly
Accelgor (1) - Can't swim, climb or fly
Mienshao (1) - Can't dive or fly
Bisharp (1) - Can't dive or fly
Braviary (1) - Can't swim
Hydreigon (5) - Can't dive
Volcarona (1) - Can't do anything besides Aerial races.
Keldeo (1) - Can't fly
Meloetta (1) - Can't dive or fly.
5 Fliers
Gen 6
Chesnaught (1) - Can't fly or dive
Greninja (7) - Can't fly
Talonflame (5) - Can't swim
Vivillion (1) - can't swim,
Pyroar (1) - Can't swim or fly
Gogoat (1) - Can't fly or climb or dive
Pangoro (1) - Can't fly or dive
Meowstick (1) - Can't fly or dive
Aegislash (3) - Can only climb and battle.
Barbacle (2) - Can't fly
Heliolisk (2) - Can't fly or dive
Tyrantrum (4) - Can't fly or dive
Sylveon (2) - Can't fly or dive
Hawlucha (2) - Can't dive
Goodra (1) - Can't fly or dive
Noivern (5) - Can't dive
Yvetal (1) - Can't swim
5 Fliers