Most things can be done solo until you hit Vice Admiral. See above comments.
If you play on a team, they are limited to 5 characters. Some missions need more than one team and that can be challenging to orchestrate.
Zones may have multiple copies (instances) which are limited to 75 players. Which seems small for something that's advertised as a MMO. So although there maybe 100,000 players online (I just picked that number out of the air), you will never see more than 74 other players at one time. The game I played just prior to STO was Pirates of the Caribbean which allows up to 250 characters. Which is exciting when you're waiting for an invasion from Davy Jones and his haunted crew.
When the game goes free-2-play on 17 Jan 2012, it will probably get extremely crowded. If you need to escape the crowds:
Check out the bottom floor of Earth Space Dock which is rarely used. (I wish they would allow fleets to rent office space there. Could have some interesting possibilities.)
Retreat to your bridge and ship's interior. Recline in your crew lounge and admire your trophies. Invite a friend or two.
Visit the Captain's Table (a station floating in space/time that opens as a veteran's reward).
