Designed by: Brian Fargo, Ken St. Andre, Alan Pavlish and Michael A. Stackpole
Influenced by: Post-apocalyptic pen-and-paper RPGs, with a bit of D&D wilderness exploration.
Series: Wasteland's sequel wasn't produced by the original developers and is widely regarded as inferior. The Fallout games, three of them as of this publication, are similar in many ways.
Legacy: The Fallout series. The Elder Scrolls series also seems to borrow from its wide-open design. Its implementation of multiple ways to solve some problems, is influential... but nowhere near as influential as it should have been.
In the early days of computer RPGs, there were a good number of games that were more wide-open in design than we know today. The lack of computer power, in a perverse sort of way, helped the cause of these games; because people didn't expect their eight-bit machines to be capable of realistic graphics and greatly-detailed world maps, developers didn't have to spend the manpower to provide them. Those days ended when games started showing that they were capable of providing a bit more meat on their grid-based worlds, and Wasteland, still fondly remembered by many, was one of the games that showed what those machines were capable of.
Wasteland has a weird position of being a kind of companion game to The Bard's Tale (a highly popular Wizardry-like game also made by developer Interplay). It contains a couple of sly references to that earlier game, and the screen has the same half messages/character roster, quarter character portrait, quarter display/battle messages system. Fights play out similarly too, down to using Bard's Tale's enemy groups and distance elements of combat.
And yet, behind the scenes, it appears that Wasteland is rather more ambitious than BT in its combat system; monsters exist as an entity on the tile-based map, and combat begins when the party enters their view.
Although the action of the fight, after actions are determined, is played as a stream of battle reports, as the monsters and the party close in for battle the player can check their locations on the area map at any time.
It's even possible to split the party up into multiple entities, each moving independently of the others in almost a roguelike fashion, and characters can even be in combat simultaneously in different areas, although as the developers note in the manual, playing the game this way is probably too annoying to be worth it.
Wasteland (Screenshot courtesy http://nuttersmark.com/blog/)
One interesting thing about Wasteland is that, despite the harsh setting, the game is actually more forgiving than you might expect. Running out of health will often not spell doom for a character. This is particularly good because there is no way to revive a dead one. So long as a character remains no worse than Unconscious condition, he'll naturally regain hit points and wake up before too long.
Sometimes combat will reduce a character to Serious condition however, and that requires rather a bit more to overcome, including applications of another character's Medic skill. If not treated, Serious characters worsen over time and eventually die. There are also ailments characters can catch that can only be fixed by visiting a doctor.
The main reason Wasteland seems to be remembered today is the depth of its game world. It was one of the earliest games featuring quests to solve that offered multiple ways of carrying them out.
Some item-based goals had multiple copies of the needed object placed in the game world, allowing players to complete them from different places. The skill system aided in this; each of the player's four characters had skill ranks in a variety of skills, ranging from brawling to perception to lockpicking to more esoteric specialties.
Skills are quite expensive for a character to begin with. The first level in a skill costs one or two skill points, but each level beyond that doubles the cost of the previous one. Skills also increase with use, however.
There are too many skills for one character to know them all to any degree of quality, but by having them each specialize in some field, the player can cover most of the bases, and the holes in the party's skill set, once out in the world, help to distinguish each playthrough from each other -- and also, if one of the characters should happen to die, to make it easier to recover from the loss.