Bear in mind, this was the 1980's. When I say mail, I'm talking mail. Paper in an envelope with a stamp. Snail mail.
Many companies advertised in the pages of Dragon magazine, and one in particular caught my eye, especially after a neat little article by the game's designer in issue #46. That game was StarMaster, run by Schubel & Sons out in Sacramento, CA. (No connection to the video game, which actually got its makers sued for trademark infringement!) It was a terrific game, and in retrospect a precursor to many of the "empire-building" computer games that are out there today. You started off by designing a planet, and your home species (you had so many "bio points" to spend on such things as lungs, limbs, different sorts of eyes and ears, powers like telepathy or psionics, etc.). You picked a technology type (for instance, you could have a technology based entirely on cold, so your weapons would be different) and an ideology, and let fly. This was a pretty old-school set-up; there was no artificial barrier keeping the older empires off your back; if you were still puttering around with 2nd generation technology, and a 4th gen empire found you, you were pretty much toast (each generation was roughly a factor of ten more powerful than the previous).
You explored, colonized, traded, invested in new technology, ships, and troops, and most importantly you interacted with the other players. Either through the monthly newsletter (which saw some really great bits of fiction and other articles by players) or directly through "message torpedoes" or the US Mail (once you got other players' addresses), alliances big and small would form, fleets would get tossed around the galaxy, and a generally grand time was had by all. And it was a cash hog, too; one movement sheet let you move 6 fleets around, but you could of course spend more money and send in more movement sheets. There were times I was spending upwards of $50 a turn, and I know some of the larger empires-- like the Imperial Dragorn Empire, or that of Valk Lifewringer, were into at least triple digits per turn. There was a background story of ancient fallen empires who were once more rising out of their stupor, invasions from neighboring galaxies, and a lot more.
It was a blast, and it was all moderated entirely by hand (I know this for a fact, as I actually worked as a game master for KSK Concepts, run by the game's original designer who happened to live 20 minutes from my house, which bought the rights from Schubel, and we spent a LOT of time converting those analog records into computer records for an upgraded version of the game).
Flying Buffalo-- now known primarily for Tunnels & Trolls, its board games such as Nuclear War, and the Grimtooth's Traps books-- was also a major player in the PBM universe, and still runs games today, as far as I know.
I tried my hand at a bunch of others; Beyond the Stellar Empire was another favorite, which placed you in command of a ship (which you got to design) and set off exploring, trading, pirating, etc. Tribes of Crane was a huge one, and the precursor to StarMaster, but I only dipped my toe into its water. Hyborian War was a more conventional wargame set in the world of Conan, and it was great fun. Renaissance was a blast, completely historical in nature, and completely open-ended. Rimworlds was incredibly detailed (and also run by someone in my home town), but I was at the tail end of my PBM days when I started, and it peetered out quickly for me. I played dozens of others as well, and actually wrote and ran my own for a short time ("Sail the Solar Winds", with print advertising in the trade magazine Flagship and everything!).
What these sorts of games bring that few others do is time. Time to savor the situation, drink it in, plot and plan. Time to have multiple conversations with folks before you need to get your orders in, and then of course the delicious wait while you scowl at the mailbox wondering why that damned game master hasn't sent your turn back. You could get that with a PBEM game, but there is also something very viceral about getting that envelope in your hands and pouring over the results in hard-copy. It's a very different experience than the instant gratification in modern computer games. It's also different than a face-to-face game, as the negotiations can get really, really involved and of course the number of potential players is vastly greater. Plus the opportunity to play a truly double-blind game is hard to come by in face-to-face games.
EDIT: Chgowiz says the following in the comments. But it's just so spot-on perfect that I wanted it to see the light of day on the post itself.
There was a magic to receiving those typewritten sheets to see what had become of you, especially to a 15/16yo kid who feels like he just became a part of something bigger.Amen, brother. I was about that same age when I started playing StarMaster, and you are so right. /EDIT
A quick search shows that there are still more than a hundred games which are run via the regular mail, including a couple of old familiar names. I might just give such searching, and consideration of getting back into PBM, a little more time.