Designed by: Jim Ward, David Cook, Steve Winter, Mike Breault (Pool of Radiance), others
Influenced by: D&D, obviously. Also Wizardry, especially in its use of specials.
Series: SSI made many of these, at least seven. SSI also made a couple of Buck Rogers games using the Gold Box engine, and the original Neverwinter Nights (an early AOL offering) was essentially an MMORPG Gold Box game. There was even a publicly-released Gold Box AD&D construction kit in the form of the Unlimited Adventures tool.
Legacy: Probably every D&D-licensed RPG to come after owes a tremendous debt to the Gold Box line.
And so we return to Dungeons & Dragons for a moment. Let's first review the progress of the pen-and-paper game between OD&D and AD&D 2nd edition, which is the version that the Gold Box games utilize.
OD&D gave rise to two different, popular branches of the game, a version called just "Dungeons & Dragons" and was handed to TSR staffers to design, and "Advanced Dungeons & Dragons," which was Gary Gygax's baby, and substantively looked like a version of OD&D with all the supplements rolled in, as well as some additions.
OD&D contained a good number of "rule hacks," weird little special cases introduced for one reason or another. For example, in the original books, elves were the only race with special status, able to play as either Fighting Men or Magic-Users, but only one at a time, per adventure. A supplement turned this into D&D's strange "multi-class" rules, giving them the ability to do both, splitting experience between their classes.
It also opened up the ability to pick different classes, and allow other races to multi-class. But since the purpose was to allow races to seem special compared to ordinary people, humans didn't get access to these rules. But then humans began to look like a fool's choice for race, so they introduced the "dual class" rules.
The result was that the rules became ever more complex, and only really understandable to people who had played from the start. Then 2nd edition came out (after Gygax had been forced out of the company), and the rules became simple in some ways, but combat became even more complicated. These are the rules upon which the AD&D Gold Box games are based.
Up until that point, TSR had viewed the burgeoning field of computer RPGs with suspicion. They had released a couple of tools for 1st edition DMs (shamefully, still the best such official tools ever produced), but nothing much in the way of games. This changed with the introduction of Pool of Radiance.
AD&D was not designed to become a computer game, and thus there are some unusual interface challenges at work here. A big advantage coming from its trying to replicate a official pen-and-paper RPG is that some aspects of the game world which almost invariably get simplified out of a concession to workability on a computer did not with the Gold Box games.
Take, for example, Vancian magic, the (in)famous aspect of D&D versions 0-3 that had wizard and cleric characters memorize spells at the beginning of an adventuring day. At "the beginning of a day," even in table sessions of Dungeons & Dragons, is a simplification; 2nd Edition established complex rules determining how many hours of preparation magic users had to undergo before beginning to memorize spells, then the actual amounts of time needed to commit them to retain them. In play sessions DMs usually, and rightly, glossed over this needless complication.
In most computer RPGs, something as weird and flavorful as Vancian magic (something that is only really effective for people who have read Jack Vance's fantasy work) would be considered too much of an interface hassle to make up for the fairly-minimal atmospheric effect from using it. The Gold Box games do include Vancian magic, even though it required a great deal of interface programming at the time to accommodate it -- the games even accurately tally up the hours spent in memorizing spells. They also track encumbrance, and even the funky multiple coin types D&D used at the time, with at least one inn even refusing payment in anything but platinum.
The games themselves are remembered fondly by many players, probably because of their strong non-linear nature and challenging play. Like a semi-directed tabletop campaign, players are given many different possible tasks to accomplish and can do them in the order the wish, or switch between them. Many of the obstacles have multiple ways of overcoming them.
Pool of Radiance (Screenshot courtesy http://www.joystickdivision.com/)
For example, to enter the dragon's lair at the end of Pool of Radiance, the player's group can either fight its way directly in, or find the laundry and dress up in disguise to avoid some trouble, or rescue a prisoner to get a password to infiltrate the castle, or find a teleporter to take the party directly to the dragon. Pool of Radiance, in particular, was designed so much like an actual D&D adventure that TSR later released a module based upon it.
Second Edition D&D was still a fairly difficult game, and the Gold Box series didn't skimp on that difficulty, but they are leavened tremendously by the save game feature. Second Edition had the most complicated character generation of all the books, so abuse of the save game feature was pretty much required to make headway.
Technically players could switch out permanently dead or ruined characters with new ones, Wizardry-style, but the newcomers would join at the lowest level allowed by the scenario, but without the benefit of all the early experience opportunities his predecessor was able to claim.
I should say a few more words about ruining characters. D&D had resurrection spells, but they were risky. If the character failed his roll he'd be left dead permanently, and even if he survived he'd lose a point of Constitution, which meant lost maximum hit points for some characters.
Additionally, there was the Haste spell, which doubled a character's actions and movement for a short time, but at the cost of a year of permanent aging. Aging is one of those things that gets thrown around as a different kind of drawback in other games, but D&D aging is fairly difficult to overcome. And the Forgotten Realms and Dragonlance Gold Box games are arranged in a sequence, allowing for characters to move from scenario to scenario. Aging a few Haste-caused years per game, characters could easily be too old to function effectively by the end of one of the later games.
Pool of Radiance gets most of its exploration interface from Wizardry. Those games with an overworld present it as single screens of wilderness, with encounters sprinkled around. One of the things that 2E brought to D&D, and works fairly well for the computer games, is its "non-weapon proficiencies," which we might know better as, simply, "skills".
The crowning achievement of the Gold Box games was their fidelity to the 2E rules, which were generally unsuitable to computer play. They are not a direct port; there are plenty of spells, even the basic ones in the core rule books, that aren't present. (Some of them, like Reincarnation, would by mere implication have made the game much harder to develop.)
Many previous CRPGs unofficially used some version of the D&D rules as their base. (One of the telltale signs, visible in Wizardry and Bard's Tale, is the use of "armor class," and whether it counts down as it's improved.) AD&D 2E was the zenith of the game in terms of independence from computer simulations. It has been observed that a likely inspiration for 3E was its suitability to adaption as computer games, and that 4E seems downright MMORPG-like.
Further reading: GameFAQs hosts an excellent guide to the 2nd Edition AD&D rules.