Diremongoose
iSpy

I have been very much enjoying the free-to-play open-beta third-person shooter Warframe. It's a mission based game with up to four players doing co-op missions against one of three factions.

Not pictured: the Infected faction
Take a look here for some fairly representative in-game footage:
Note the mod system has been completely overhauled now. Mods are now droppable loot, making the game MMO. The game definitely has some bugs, but is getting patched every couple of days.
The new system looks like this:
You pick up 'cards' as drops from enemies and fuse unwanted or duplicate mods into better versions.
The game has a variety of different mission types and objectives as you run through randomly generated maps towards your objectives. There are a variety of fun weapons to craft (or buy for real money if you're impatient).
What can I say? It's free, it's a small download, and it's fun without the need to spend cash. Grab a friend and give it a try!
Oh yeah, wall-running and jumping and other extreme acrobatics are a thing: you're space ninjas/samurai after all.