Fun things to do with a buddy:
[quote name='Spuz from Teamxbox Forums']
Recon missions
One player climbs an extremely tall building, chooses a vehicle, and tells the other player information (location, colour, type of vehicle, etc.) about it. The other player, of course, has to track down the vehicle and take/destroy/kill the driver, etc. To further extend this, if it is a 'take' mission, the goal may be to take it back to the Agent HQ. Meanwhile, the 'recon player' comes down from the building and must STOP the retrieval of that vehicle at all costs!
Good cop, bad cop
One player causes as much mayhem and destruction as possible, while the other player's duty is to stop him at all costs.
Ramp it up
One player drives around with the ramp truck, while the other continues to ramp off of it; sillyness naturally ensues!
Fireworks!
Setup a line of satchel charges across the wall of a building, and watch the display! (This will be even better if/when they come out with the additional video editor! Send your best displays to your friends on Xbox Live!)
Sniper Evasion
As you may have guessed, one player is the sniper, and the other one is the victim.
Foot Vs. Ferrari (by ManBeast)
Both players race to a point on the map, but one person goes on foot, using rooftop transportation, and the other takes a vehicle, fighting through rush hour traffic.
Speedzone Drop (by i-candy)
One player speeds by in his vehicle, and the other player attempts to drop onto the vehicle as it speeds by. Increase difficulty by choosing faster cars, or higher buildings to jump off of.
Death/Defying Jumps
Both players jump off the same building and shoot each other on the way down. Whoever lives when he hits the ground, wins.
Roullette
Cars are lined up along the street, and satchel charges placed under one of them by one player. When the other player chooses a car, the satch is exploded, and then the remaining cars are left. Take alternating turns until one player or the other is in pieces, or until there is only one car left (which, I suppose, would be a tie)
Car Flipping
By strategically placing satchel charges, try to get a vehicle to do the most spectacular flips in the air. This can be modified further by allowing each player to have to use a certain number of satchel charges, etc. Also useful when determing "heads or tails"; tails if the car lands upside down!
Tag! (by TAPOUT)
Flip a car (see above) and call heads or tails to determine who is
IT, and then chase the other player down! It only changes sides when the other play is touched
physically by the other player.
Hot Potato
A modified version of tag. Get the cops to attack both players at once, and then during being attacked by the cops, play a game of Tag. If you die when you are IT, you lose!
Rooftop Tag
Another version of tag. This time it's limited to rooftops only! If your feet touch the ground, you lose! (Hint: Kick the other player off the roof.)
Catch Me if You Can (by Dangerous)
One player is in a car, the other is on foot. He must stop the car at all costs. This can be modified by restricting it to a certain area, or restricting certain weapons (picking up and throwing, or kicking the car to destroy it?)
Hide and Seek (by Monster Tard)
As the name implies, you hide and seek! Could be modified with a time limit, and when the time limit runs out, the hider will gain a point. (Hopefully you can disable the view of the other person in the radar as well!)
Pictionairy (by Silentstriderm)
Using bullet holes, bodies, vehicles (could be done looking down from the top of a building), or any other in-game item, one player creates a picture while the other player tries to guess it.
Stacker
Each player tries to stack his pile of cars higher than the other player.[/QUOTE]
http://forum.teamxbox.com/showthread.php?t=503044
There are some interesting ideas for extended gameplay fun.