Well...
The fighter/mage/thief in previous (pre 3.X) editions of D&D was a nifty class that allowed a player to do most anything, but as per older versions of D&D (rather I should say AD&D), any XP you earn would be split 3 ways, making for an extremely slow character progression. The only other variation on the 3-multi-class combo was the cleric/fighter/mage. For the F/M/T, only elves & half-elves could select this as a multi-class option; & only half-elves could choose the C/F/M combo.
As for an archetype, the only example I could guess would be the Gray Mouser, though he's human. Otherwise, I'd gather that it was an extention of the "elf" class from earlier versions of D&D, which was essentially a fighter/mage with some unique racial abilities added on.
The 3-way multi-class PCs were a great boon for a small group of players--it was a way to "cover all the bases" for AD&D games. Also, it was a way to have "back-ups" in larger groups that weren't doubles, per se.
For example, a group of 6 players could have a fighter as the main combatant, a mage as the main arcane spellcaster, a priest as the main divine spellcaster, and a thief as the main trap disarmer/lockpicker, plus have a fighter/thief/mage and a fighter/cleric present as "back-ups"--basically characters able to cover when the single-focus PCs are, for example, running low on spells or getting overwhelmed by opponents.
However, the race/class restrictions with AD&D pretty much made elves & half-elves very popular choices for players who wanted to multi-class, esp. if they wanted to select mages for multi-classing. Dwarves, halflings, gnomes, and half-orcs pretty much were stuck either being fighter/thieves or fighter/clerics (though, IIRC, half-orcs could be cleric/thieves, and gnomes could be multi-classed illusionist specialist mages). The slower movement rate didn't help the smaller races much, nor did the chance of magical malfunction for gnomes & dwarves (well, from what I could tell/have experienced, at least). Humans were popular since there were some human-only classes, & since they didn't have to deal with level limits at all (&, if a PC was lucky enough, he/she could opt to dual-class if his/her stats were high enough).
In 3.X D&D, it is feasible to go with such a multi-classed character, but more likely than not, it'd be either a "jack of all trades, master of none" type of character, or it'd be a a character of 1 class who dabbled a bit in a couple of other classes.
There are some PrCs that augment certain multi-classing choices, like the arcane trickster for rogue/arcane spellcaster combos, the mystic theurge for divine spellcaster/arcane spellcaster combos, and the eldritch knight for a warrior-class/arcane spellcaster combos. But, more often than not, it's just for a 2-core class combo.
The bard class is the closest thing that I can think of for a "jack of all trades, master of none" sort of character--a skilled character with some weapon & armor abilities, some spellcasting ability (which isn't penalized for wearing armor), and some healing spells even though the bard's an arcane spellcasting class.