If I remember correctly, Dreamcast's Quake 3 or Unreal Tournament was playable over LAN. Might even have been compatible with the PC version.
I can't remember for Unreal, but I'm pretty sure that Quake 3 had cross-platform play with PC if you ran a specific patch on PC. There are still people playing Quake 3 on DC online, and some servers still up.
Mario Kart Double Dash lan play, I remember playing playing that over the internet back in 2004 using Warp Pipe. It was just about playable with a 15kb/s upload, which is all I had back then. I think the absolute best was 30kb/s on some ADSL connections. I got my GC BBA from Lik Sang as i dont think they were ever sold in the UK, if they we're I had never seen them anyway. Good times playing Mario Kart with a friend in London and another friend in the Netherlands. I bet Mario Kart DD would play perfectly today over the internet, it's really awesome to see people setting lans up in public to play!
I'd love to, but my GCs + BBAs are sleeping in a dark cellar across the ocean at the moment. Although I guess I could buy one here plus a BBA, they aren't looking that bad in pricing considering everything else is going up like crazy lately.
I wonder if PAL / NTSC / JPN copies can lan play with each other? It would be nice to get a few games going, just really awkward across multiple time zones and the potential different regions of games. I guess if it does work on devolution using a hack Wii / Wii U that would solve the potential region issue. That would be interesting to try, especially if Devolution works on the Wii U's vWii (don't own an actual Wii, but have a Wii U).