I am using "Hero Points" is a generic term for a type of mechanic where the player can spend from a limited supply of abstract points to gain successes on actions, cause background events, or perhaps manipulate the plot in other ways. These are generally a meta-game resource -- i.e. they are a resource for the player, which doesn't represent anything in particular about the character.
The first Hero-Point-like mechanic was an optional rule in the original Top Secret game (1980). That has an optional rule entitled "Fame and Fortune Points". Either type of point can be spent to reduce a fatal wound to a non-fatal wound (only), or prevent unconsciousness in hand-to-hand combat. A character's Fortune Points are determined by the GM secretly rolling 1d10 at the start of the campaign. The player never knows how many are left. Fame Points are known -- 1 Fame point per level raised. As written, this is little more than a special damage mechanic. The only choice is whether to spend a point to prevent unconsciousness, or save it for later.
The real pioneer of this technique was James Bond 007 (1983). This used "Hero Points" as a central mechanic. Players gain 1 Hero Point every time you naturally rolled a critical (Quality Rating 1) success, which is 10% of all successes. You can spend 1 or more Hero Point on any roll, where 1 point turns a failure into a success or improves the Quality Rating of the success by 1 -- QRs going from 4 (worst) to 1 (best). Incidentally, this encourages players to try to show off in their strong skills (since that maximizes the chance of a critical success), which is a nice bit of genre emulation. Hero Points could also be used to modify the environment, though this was not explained in detail. The rules on this were:
If your GM agrees, you can spend Hero Points to affect the environment in your character's favor. James Bond always seemed to have at hand the things he needs, and Hero Points may be used to have your character discover something useful in an emergency. Changes in the environment must be within reason; you cannot, for example, use Hero Points to change a snowstorm into balmy weather.
As a general rule of thumb, the more fantastic the action you want your character to perform, the more Hero Points you will have to use. The GM is the final arbiter on how many Hero Points must be spent at any time and on the changes that may be effected by Hero Points.
EXAMPLE: In The Man With the Golden Gun, when Bond is in a small river boat he seeks to escape the kung-fu fighters, he seemingly runs out of fuel (in game terms, the player rolled a 100 for his Pursue/Flee maneuver). A small boy jumps in his boat, trying to sell him a souvenir elephant, and just happens to be able to open the fuel spigot, allowing Bond to escape. In a similar situation in play, the player would use Hero Points to have the 100 result (a failure) changed to a Quality Rating 4 and thus continue his character's escape.
TSR's Marvel Superheroes RPG (1984) had "Karma Points" as a central mechanic -- which worked similarly to Hero Points, but had more complex rules for gaining and losing points. Before any roll, you can declare you are spending Karma. Then after the roll, you have to spend Karma Points equal to the difference between your roll and what is needed for success -- with a minimum of 10 points. Karma Points are gained by stopping crimes and acting as a good citizen, and can be lost by unheroic behavior or neglecting your normal life and relationships. For example, you lose all Karma Points for killing. This is maintaining classic comic-book morality. In the original game, Karma Points are not used for character improvement -- in fact, there is no character improvement.
The DC Heroes RPG (1985) also featured "Hero Points" as a core mechanic. These have broader uses than the previous ones, however. Characters can spend Hero Points to gain initiative, temporarily increase attributes and powers, or reduce damage taken. It also costs Hero Points to build gadgets and to buy new powers. This merges the effect of experience points and hero points, which were separate in JB007.
The Ghostbusters RPG (1986) had similar "Brownie Points" which could be used as experience points to improve the character stats, or to guarantee success on a roll, or to reduce damage taken. Incidentally, this was the origin of the "D6 System" used in several later efforts by West End Games.
This system evolved into the Star Wars RPG (1987), which had both "Character Points" and "Force Points". Spending a Force Point would double the number of dice you rolled for an action, and had to be declared before the roll. These are restored at the end of the adventure depending on how they are used. If the action was unheroic, the points is permanently lost. If used heroically, it is restored. If used heroically at the dramatically appropriate moment, it is restored plus an extra point. This is a big change, because there is thus no penalty for using Force Points heroically. Players are thus highly encouraged to spend them before the end of each adventure.
Character Points in Star Wars are normally used as experience points to improve the character. However, they can also be spent as a last-ditch guard against failure (especially defense). You can declare after a roll that you are using a CP, and you get to add one extra die to that roll. This is very inefficient, however. If used regularly, this could become a spiral -- as characters who need to save themselves spend off their experience and thus become relatively weaker and more in need of saving.
Ars Magica (1987) has Whimsy Cards as an optional system -- mentioned in the basic game book but with the cards sold separately. Each player gets a set number of cards at the start of each session, and playing a given card has a specific effect on the story. For example, cards include "Bad Tidings" or "Something Missing". The player then gets to detail what the event is. This is a very different effect, moving away from just modifying rolls or stats and instead actively controlling background events. In addition, this is like Force Points in that cards are never permanently lost, so the players are strongly encouraged to use them every session.
The Prince Valiant RPG (1989) has "Storyteller Certificates" as a rule for the advanced version of the game. A player gains one certificate for GMing a session (assuming shared GMing, obviously), or they may be awarded by the current GM for "good acting or other reasons". Spending one can be used for one of 13 Special Effects, ranging from "Save in Combat" to "Find Escape Route" to "Kill a Foe in Combat". So these are more flexible than Whimsy Cards, but are gone permanently if spent.
Shadowrun (1989) has a single pool of "Karma Points" which are used for magic, character improvement, and changing rolls. As a single pool, this put a focus on it as resource management, but that fit with other aspects of that game.
By 1990, hero point mechanics had become fairly ubiquitous and appear in a great many RPG designs. For example, a mechanic of this type became a central feature of White Wolf's Storyteller house system as "Willpower". Thus, I cannot cover all the examples. Instead, I will highlight only a few.
Torg (1990) and Shatterzone (1993) both used a deck of cards called the "Drama Deck" as more central mechanic than the occaisionally-used Whimsy Cards. Drama deck cards served a dual purpose: acting both as initiative/position in combat through random draw, and also as resourced which players held hands of and could even trade during play. Later games like Castle Falkenstein (1994) and Dragonlance: The Fifth Age (1998) featured playing from a hand of cards as their central mechanic.
In Vampire: The Masquerade (1991) and other Storyteller games, PCs can spend a point of Willpower to do one of several things: (1) gain an automatic success on a single action, (2) override imposed behavior for a turn such as madness or fear, or (3) ignore wound penalties for one turn.
I should also note Theatrix (1993). This is a diceless system which has Plot Points as a central mechanic. Plot Points are required to activate Descriptors and Personality Traits. The player may spend a Plot Point for an automatic success if the character has an appropriate personality trait which would be involved. More interestingly, a character will have a Descriptor like "Master Criminal" -- but in order for that to be dramatically effective in a scene, the player must spend a Plot Point to activate the Descriptor. Lastly, if the player may use their Primary Descriptor and spend Plot Points to make their character's statements true. i.e. The player of the "Master Criminal" may spend a point and declare that he has found a secret entrance to the base. Plot Points are gained by initiating and completing sub-plots.
There are a few general design decision which one can draw out from the variety of different individual mechanics:
1) Only for control or combined control/improvement?
This is a tricky one. If the hero points can also be used for both control and character improvement, that potentially motivates a player to hoard them rather than using them in play. This is good if you want them used rarely. However, in a competitive environment, it can result in a spiral effect. i.e. A player who spends points is then less capable compared to the others, which may require him to spend more points to keep up. More generally, this implies a range between (1) the player who never uses points for control and whose character slowly becomes much more powerful than the others, and (2) the player who constantly takes control using points but never advances, probably dominating play at first but then dropping out of the picture. You should think if you really want both these types in the same campaign. If you don't want them, then you should probably have separate Hero Points and Experience Points. i.e. Don't give the option of that tradeoff.
2) Permanent loss or per-session/per-adventure use?
There are two important decisions here: are hero points a permanent resource or a temporary resource? A temporary resource means you get a set of hero points (or cards or whatever) at the start of each session, and if you don't spend them by the end, they're gone to be replaced by a new set next session. This is the approach of Force Points in Star Wars, where as long as you act heroically you always get them back -- possibly with interest. This effectively rations their use, and thus forces players to use them regularly and prevents hoarding/purging.
A permanent resource means that points can be accumulated from game to game. If they can be spent as experience, then see above about the effect of hoarding. However, if they can only be spent on control, then the most that may happen is unevenness of control. i.e. A player may completely overturn or dominate things by spending a pile of points at once, but then may be weakened for a time afterwards. The James Bond 007 RPG has accumulated hero points, which allows for such behavior.
3) How are points gained and/or restored?
This is an important question, which is similar to the issue of how experience points or other mechanical rewards are determined. What behavior are you trying to discourages and/or encourage? If you don't have a specific effect in mind, then it is quite valid to make the points a single flat rate (i.e. 3 points per session). Also, bear in mind that reward for subjective judgements like "role-playing" or "story" depends on whoever is doing the judging. i.e. If the GM is the judge, then you are rewarding for playing the way the GM wants. If judgement is by vote among the group, then you are rewarding popularity.