EVE Online

free-to-play, with optional subscription (?)

EVE Online is the enormous space-based MMORPG from CCP Games, launched in 2003 and famous for turning a virtual galaxy into a sandbox of trade, politics, piracy, exploration, industry, and warfare. Players can specialize in mining, manufacturing, commerce, exploration, combat, or simply becoming the person who makes somebody else's day considerably worse. Its player-driven economy and organizations have produced some astonishing stories over the years, including massive battles and elaborate acts of corporate espionage. The learning curve can be intimidating, but the freedom is extraordinary. In EVE Online, losing a spaceship can be painful; discovering that your corporation has lost an entire fleet is apparently a legitimate form of entertainment.

“Player-created empires, player-driven markets, and endless ways to embark on your personal sci-fi adventure. Conspire with thousands of others to bring the galaxy to its knees, or go it alone and carve your own niche in the massive EVE universe. Harvest, mine, manufacture or play the market. Travel whatever path you choose in the ultimate universe of boundless opportunity. The choice is yours in EVE Online.” - CCP Games

EVE Online key features:

a sandbox MMORPG like no other: mining, fighting, exploration, solo missions, etc.
a player drivern universe where player alliances form and shatter
one of the nicest communities in MMORPGs
don't like fighting? Be a space miner, trade commodities, manufacture products
no multiple servers: play in a single huge universe