Thread's so good it gets better every time someone posts it. Snark aside, I've got a few ideas, but they always seem to come back to the long-forgotten genre of the trade sim and its cousin the city-builder.
Anyway, here's the concept: Anno series meets Port Royale meets Colonization. The year: 1587. The place: Roanoke Island. You are a settler in Walter Raleigh's ill-fated Lost Colony, come from England to make your name in the New World. It is here that the tutorial takes place, as you're taught how to build farms to feed your population, fortifications to keep the Natives at bay, and industries to grow cash crops for export back to Europe. All simple, straightforward stuff, but after the tutorial a cutscene explains how history diverted.
Seems that when the Lost Colony ran out of supplies, a mutiny split the colony in two. Fierce fighting led to the death of most of the men, and when the dust settled you and your loyalists built a boat and set sail southward, finally setting up a freebooter/pirate settlement near what is today Savannah, Georgia. Knowing that if your English heritage were discovered by the Spanish colonists in St. Augustine you'd be slaughtered, you decide to build up a settlement and get a ship to sail around the Caribbean, recruiting (sometimes at swordpoint a la Tropico 2) a multinational band of outlaws and castoffs from towns, villages, and pirate coves. Friendly settlers in Dutch and French towns will provide trading partners as long as you don't try to raid their villages.
Meanwhile, the Spanish Armada sinks on schedule in 1588, giving you a chance to begin terrorizing the Spanish Main...or a visit to the viceroy can get you peace at the expense of earning the wrath of Queen Elizabeth. Win a few battles against the Spaniards, however, and Jolly Olde England will send you regular shipments of indentured servants and petty criminals in exchange for your fealty, and having an export market in Europe for colonial goods can make you plenty of money if you don't mind having minimal naval support and having to constantly worry about the Spanish threat.
Lost Colony (working title) would bring together all the best elements of city-building, trading, and naval combat (using Empire: Total War's naval combat graphics engine with a little more realism and better AI.)