So far, there is a champion that has a giant sword to slam into enemies for each region.
Except Void and Zaun...
Demacia - 
The only champion that has a signature slam that is 450 IP. This champion is great for a Fighter role and Tank (due to 2 tank passives).
Noxus - 
Darius is the only one to have his slam on his ultimate. His ultimate can be used twice in a row. Darius is one of the few champions to be allowed a bleed effect.
Piltover - 
Jayce is one of the few champions to get 6 abilities. He is more known for his long range powerful shots but is also fierce with his hammer that has 2 slams that can even combine into 1 powerful slam. He is also the only one to use a hammer. He is also the only ranged Fighter.
Ionia - ?
Nothing...
Freljord - 
Tryndamere is not thought to have a slam, unless his Q's passive gives him full rage; he then slams his giant sword down on his enemies. Tryndamere is the only one to use rage.
Bildgewater -
or ?
Nautilus could fit the definition since he has a slam with his anchor but its more or a smash than a slam. Tryndamere is iffy just the same, but in Tryndamere's defense, his passive is from his Q and he puts effort into it. It's more up to you guys to decide, really. Yet I would love a original idea to pop up from Bildgewater since it has had no love for a while.
Zaun - ?
Currently, I don't think any fit the needs to be like the others.
Void - ?
Again, none fit the needs.
Shurima - 
His Q is a slam that he uses with a large weapon. He is the only slam champion that is part animal.
Now, what made me pick them is not only their slams, but how similar their kits where to each other.
[P] Bonus health regen
[Q] Slam + Movement Speed Bonus
[W] Armor and Magic Resist
[E] Spin
[R] Execution
[P] Bleed
[Q] Spin
[W] Bonus Damage + Slow
[E] Pull
[R] Slam

[P] Movement Speed Boost [Q] Slam/Shot [W] Small Area Damage/Multiple shots [E] Spin/Movement boost + shot boost [R] Change (Slam/Armor Penetration)

[P] Rage [Q] Heal (critical Slam) [W] Spin [E] Slow [R] No Death

[P] Slam [Q] Pull [W] Shield [E] Slow [R] Slam

[P] Life Steal [Q] Slam [W] Damage Area [E] Slow [R] Bonus Health
All of these champions are Fighters and have these in similar.
- a Slam
- movement bonus or movement slow
- damages a small area (usually with a spin)
If Riot were to make another one of these champions, this is what I believe they would have. Zaun and the Void could use on of these guys. Not sure how this would work for the Void but Zaun could be cool, and lets not forget about the Shadow Isles.