Here's a bit of nostalgia for you: Sven Co-op [official site] is now on Steam. The seventeen-year-old Half-Life mod is available as a free standalone game, and—thanks to a fair bit of generosity on Valve's part—includes all of the Half-Life campaign maps. For free.
That means you can head to Steam, download the game, and start playing co-op Half-Life right now. Again, for free. No need for you or anyone you're playing with to own Half-Life proper.
The main difference with Sven Co-op is that Half-Life's been rebalanced for two players, adding more enemies and some two-person puzzles. Also: improved enemy AI, additional weapons, a revive ability, new monsters, a new physics engine, high-definition models, and an optional third-person camera.
Phew. Okay, other than that, it's Half-Life. You can also play through Blue Shift, Uplink, and Opposing Force, were the inclination to take you.
The standalone Steam release launches alongside Sven Co-op version 5.0—yes, a seventeen-year-old mod is still in active development. Here's a trailer, though it's a bit hard to tell what's new and what's not. If you want the nitty gritty details, you're better off reading through the changelog, like it's 1999 all over again.
And if you're tired of Half-Life but want to indulge in some no-holds-barred '90s gaming, there are apparently "well over a thousand custom co-operative scenarios" for Sven Co-op at this point. There's no Steam Workshop support yet—it's slated for a future update—but there's plenty of old-school fun on the internet if you're willing to look around.