What is 'NGC'?

It could be any of a number of things, depending on your context; National Geographic Channel, National Guideline Clearinghouse, National Gallery of Canada, National Graduate Caucus, Spiral Galaxy NCG-4565, New general catalogue, New Generation Computing Inc., Northrop Grumman Corporation...and many more.

If you found it on a star map, it almost certainly means "New General Catalogue," which is a listing of so-called "deep sky objects" put together at the end of the 19th century. There are several thousand objects in the catalogue; each is assigned a unique number. The NCG objects include galaxies, nebula, clusters, etc. The NGC is a much more extensive collection than earlier catalogs such as the Messier catalog.

Of course, it could also mean "Nintendo Game Cube" - a previous generation games console.