STO server info from official forum chat
The current plan calls for a single, worldwide server - though they may shard as need be. It seems that US and EU will play on the same servers, though, and I would imagine Cryptic is taking steps to ensure that ping times are good for both geographic areas. For the record, EVE Online manages to be fairly playable even from the far parts of the US, and its servers are based in London. I would imagine STO can do similarly.
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There will be one "server". Everyone technically plays in the same universe. To prevent too many people in one place, they have multiple instances. This part is similar to other games, like WoW, that have a dungeon that you can access, but other people get their own version when they access it. Just as a generalized, completely made-up example: 500 people are at Deep Space Nine. You arrive there. You don't see 500 people. You see maybe 100 people. The maximum in one "instance" would probably be 150. The other 400 people are split up into other exact duplicates of the same place. If you find out you're in Deep Space Nine 3 and your friend is in Deep Space Nine 1, it only takes a few clicks for you to switch to their instance. In this case, the 100 people you can see get replaced with a different 100 people, but everything else remains exactly the same... NPCs, quests, etc. Really, in my experience in CO, you don't even notice except for the few seconds of "I'm here, where are you? Oh, I'll switch instance". But I feel this is a major improvement on the many isolated servers, like WoW, that was the most common practice up until now. And non-instanced single-server games can be too laggy in places people gather
