We'll look at plenty of digital adventures shortly, but first up its worth noting that infinite Star Trek tales await if you go the tabletop RPG route rather than pulling up a PC or console game.
Right now Star Trek Adventures is the one to keep your eye on, whether you just want the main rulebook or are willing to shell out for the the ludicrously expensive (and ludicrously awesome) Borg Cube version. That release for the uber-fan includes its own Borg ship complete with drawers to hold the books and dice.
This latest iteration of the Star Trek pen and paper RPG comes from Modiphius, a designer known for making high quality and visually appealing RPGs like the latest Conan, Fallout, and Mutant Year Zero tabletop games.
Not a fan of the Modiphius rules system, or prefer something a little more classic? There have been plenty of other versions over the last few decades that can still be readily acquired second hand.
The sadly defunct FASA (known for classics like Earthdawn, Shadowrun, and Battletech) released dozens of supplements throughout the '80s before The Next Generation even hit TV, and many of them can still be found on Amazon or eBay.
If you prefer a system more directly derived from the TV series, the hard cover Star Trek: The Next Generation core book released by Last Unicorn Games in the late '90s had a solid rules framework as well.