Hi Freebird, there's several genre of games where you can find lots of multiplayer action, namely Football, Tennis, Olympics, Golf, as well as Vehicle racing. I'm sure some of the Tycoon games have online capabilities as well.
regards
Whiterabbit
p.s.
I've just gone through my collection of DVD based games and am actually quite shocked at the number of games that involve killing. Still, here's a list of those games I found that have multiplayer action but no killing - (theres more , but I have things to do):
Sega Rally:
Flatout ultimate Challenge plus the first two in the series - Flatout and Flatout 2, both of which are available from GOG - well the first one is :)
Burnout Paradise: The Ultimate Box:
All the Colin McRae series (Colin McRae Rally, Colin McRae Rally 2.0, Colin McRae Rally 3, Colin McRae Rally 04, Colin McRae Rally 2005 and the best on in my opinion Colin McRae: Dirt. And an obituary release this coming September 09 Colin McRae: Dirt 2
All the Need for Speed series, especially the last four. There has been 16 Need for Speed releases since the first one in 1994, the best of these are Need for Speed: Most Wanted, Need for Speed: Carbon, Need for Speed: Pro Street and the latest one Need for Speed: Underground. The next one is slated for mid September this year and is called Need for Speed: Shift
Racedriver Grid - (this is a traditional racer with a large modding community. There's loads of extra tracks downloadable for free)
Race 07 (ditto with this traditional racing game as well)
GTR2
Test Drive Unlimited This is a free roam driving game where you can race if you want or just drive around. They have recreated the Hawaiian Island of Oahu, with over a thousand miles of roads to explore and race along. The game looks pretty good, though newer games such as Fuel (just released last Friday 26th June) are being released with even more realism.
Torino 2006 A really good winter sports sim, need an X-Box controller to play properly.
Motocross Madness 1 & 2 Although quite old, both games are really good for their age (graphically speaking) You can wander around the environment in some of the modes. The trial bikes handle like real ones (almost)
MotoGP: Ultimate Racing Technology
Some of the Tycoon series such as Railroad Tycoon II & III You can get the first Railroad Tycoon for free as it's abandonware now. (see the game synopsis. Tjhe other two are avalable via Steam. There's a special offer on at the moment for both titles as well as a Sid Meier's Train sim as well. Check out the 2K deal for all three games)
Theme park world Cartoon style, but a lot of fun
Tiger Woods 2007 & 2008 (I don't have earlier or the latest, but I presume they are online as well. the latest one even has some new additions that make it a must have for Golf fans.
Beijing 2008(this is quite a good Olympics game with loads f different events to race. You do need a PC version of the X-Box controller (though you can actually use the official X-Box controller with a USB attachement
Extreme Paintbrawl 2
Shawn White Snowboarding
The Myst Series ((Myst, Riven, Myst III: Exile, Myst IV Revelations and Myst V: End of Ages plus URU)
Microsoft Flight simulator 2004
Of the ones above if you check in the Wheeled Games thread (somewhere in the Games discussion forums) you'll find a list of racing related games I offered to give away for free, some have still to be claimed - though I did have a clear out recently and took a lot to the charity shop) I also have a spare copy of Myst II: Exile which I'm happy to give away (I managed to get a hold of Myst: The Collection which alreay had Exile inscluded). I've not even touched the arcade section of my collection, most of which are non violent games and involve puzzles mainly. (for example Linerider 2: unbound)
I think most Car/Vehicle related games have multiplayer action, though I think maybe you wouldn't want to try either of the Big mutha Truckers games as it involves vehicle jacking and illegal actions. I've got a pile of older vehicle racing games that I've not decided what to do with such as Total Autobahn Racing, Crashday, Overspeed, Taxi Racer London 2, Midtown Madness 1 & 2, Super Taxi Driver, Doomsday Racers and London Racer (some of those titles are included in the giveaway list I provided in the Wheeled games thread)
I hope you can find something in the titles I've mentioned above. you should be able to check You Tube videos of most of the games I've mentioned. :)