The Gaming Den

There was the Playstation 3/PSP game "Eye of Judgement" where you placed monsters down on a 3x3 grid.

Gundam War also has an "Earth" and "Space" zones.

I believe the latest 40k card game has battlezones but don't know much about it. Not sure how the Warhammer Fantasy card game plays.

What else is out there? Any card games where movement between zones is interesting?

The 40K card game, Call of Cthulhu LCG, and Star Wars LCG (all made by Fantasy Flight) have locations you fight over, although for the latter two locations are sort of temporary affairs.

PC games Spectromancer and Soulforge have lane-based combat, but relatively little moving.

The physical version of the Adventure Time card game also has lane-based combat with relatively little moving.

The Might and Magic card game on the PC has a (2x4?) grid you can place your minions in and move them around on, and all minions can move.

The old Star Wars CCG by Decipher (and it's derivative game with the IP scrubbed, entitled simply 'Wars', IIRC) featured a variety of player chosen zones to fight over.
The Lord of the Rings LCG (Fantasy Flight, again) features a quest system and areas to explore.

In L5R, each player has 4 provinces, and when attacks happen, players commit infantry to attack or defend provinces and then players commit cavalry to attack or defend provinces. There are cards and abilities that can move units from one province to another once the battle starts, and at the end of battle a province is destroyed if the attackers have enough more force than the defenders in that province.

In Shadowfist, you play sites into locations, and each location can have just two sites in it. So if you want more than two sites (and you need at least five to win, so you do), you need to start creating additional locations, which you can do just by playing a site next to the sites you already have. Characters are at a particular location, and they can tap at any time to move to an adjacent location. They can choose to block characters attacking targets in the location they are in, and not other places.

In both cases this leads to an inherent situation where it is easier to defend when you are behind. You have less provinces/locations and can thus cover your defensive needs with less defenders.

-Username17

Something similar to L5R's province stacks was at play in the original Netrunner, where the Corporation started out with 3 nodes (Hand, Library, and Discard) and could then create as many more as they wanted, each with their unique defensive IC in front.

Rage has zones too, as I recall, representing battle areas and the Umbra.

I believe zone control more or less defines Doomtown.