future cop is pretty cool, at least the memories. (the 2 player vs-mode where you capture turrets and have to get a tank into the enemy base..no idea what rest of the game is like)
There are tons more of good same-monitor games, but most are pretty old and sometimes it shows :/
Superlow resolution,clunky controlls, no support for (modern) gamepads or just do not work..
I mean liero for example was great but not sure if I could still enjoy it today.
If you do not mind, then maybe also try:
Tank Arena (super original name, appearently the creator later worked on killzone for ps3)
http://www.jrouwe.nl/tank/
not sure how good this runs on modern computers, but was great fun.
2d tank combat with lots of levels and game modes.
Raiden 2
(cant find link)
shot'em up scrolling shooter
Clonk
http://www.clonk.de/?lng=en
There are several versions, do not remember which was best.
you are supposed to build a town, mine for resources and all that.
Somehow all the dudes always end up drowning in some mineshaft or exploding each other with firestones
Hmm, all these games are made in Finland... Apparently so is Trine - is this just my limited vision or did ~all best splitscreen PC games come from here
also GeneRally...
http://alternative.gene-rally.com/
...and PUM
http://milzer.org/?page_id=28
think soldat, but much simpler and over the top.