Designed by: Masaki Norimoto (original), Takashi Hasegawa, others
Influenced by: Fighting games, Final Fantasy
Series: A huge number of games starting with the SNES and moving forward to the present console and handheld generation. Most recent U.S. release was Tales of Vesperia on the Xbox 360 (coming also to the PS3.)
Legacy: Low so far.
There was a time midway through the SNES' life that action adventure games and RPGs had a brief love affair.
These days, there are many games that would best be considered action adventure games, or first-person shooters, or even driving games, that host a type of experience system and statistic improvement. But RPG games that incorporate action elements most commonly get shunted off to the "action adventure" category.
The leeching-off of RPG elements into the greater field of video games has helped to encourage a strange definition of terms: because so many games could be considered role-playing games now, the CRPG genre is now being defined by those elements that other genres are least likely to steal.
And so Zelda games, which mostly don't have an experience system and have mostly action-oriented play, get called "action-adventure" games, even though practically everything else about them is RPGish.
The one thing, however, that seems to guarantee a game with action battles will get labeled an RPG is some application of statistics to the fight. One example: few deny that Secret of Mana is an RPG, but the thing about it that most distinguishes it from action-adventure games is that, when you hit an enemy with your sword, you might not actually hit.
Instead, the enemy gets a chance to be missed anyway, or not damaged. The lack of damage is explained on-screen with a hasty dodge animation. And conversely, if a monster is seen to bite your character on-screen, there's also a chance that your character will instantly dodge out of the way, regardless of whether you hit any buttons.
Tales of Vesperia
These chances, of course, are largely determined by level and attribute scores, which is kind of odd when you think about it. The main purpose of stats in a role-playing game is to determine whether an action succeeds in the absence of other factors, but in an action game those factors are no longer needed; the player's skill can determine whether an attack hits or not. To then go in and add a further chance of failure in addition to that provided by the real-time motion of the enemy seems redundant.
Anyway, I mention this because Namco's Tales series are much this kind of action-RPG thing, although it fights tend to be more similar to a fighting game than Zelda, right down to giving the characters attack combos. This hybrid battle system is what draws players in; in Japan, the series is also loved for its strong cast of anime-style characters, a feature that may be less endearing to a broad audience in the West.