The largest battle ever in EVE Online took place today in the system of LXQ2-T, which topped out at over 3,200 participants. Per Massively:
The number of players in the system peaked at over 3,110 pilots, with alliances from the Northern Coalition political conglomeration facing off against the Russian power block from the drone regions. Lag began to set in at around the 2,400-player mark, with pilots facing several-minute delays on warp commands and module activations.
Note especially the bolded part. Don’t interpret this to mean “there was no lag until there were 2,400 players in system,” but still… most other game clients start to choke when the number of players in the vicinity gets above a few dozen. WoW crashes outright if there are too many people in Ironforge. Yet EVE manages 3,000+ people in a single system, and while I’m guessing the lag was horrendous, no fatality was scored on the server. As far as I know.
Note also that this is almost certainly the largest online battle ever, anywhere. By a lot.