Unknown Armies has The Fool as an avatar, where you can be happy go lucky, find the right item at the right time, avoid damage by accident, be in the right (or wrong) place at the right (or wrong) time.
This troper once played an Unknown Armies game as a Fool and ended up saving three characters' souls by tripping and falling in the right place at the right time. It is an extremely powerful archetype.
Also dangerous to be around, though - as that damage you avoid by "dumb luck" has to go somewhere...
Mage: The Awakening associates the Acanthus Path with the Tarot card of The Fool. Members of the Path have a natural affinity for Fate magic, meaning they can get really lucky.
Dungeons & Dragons introduced Luck feats and the Fortune's Fool prestige class late in 3.5. Although the flavor of it has them surviving in day-to-day life based purely on being incredibly lucky, the mechanics just let you re-roll dice a lot.
Everway, which uses a modified Tarot deck as a game play mechanic, has an Alternate Character Interpretation of The Fool: a cross between a court jester and a wanderer. The Fool is free to do or say anything and get away with it, because no one takes him too seriously, and he's not tied down with responsibilities. This doesn't imply stupidity or luck. More like "Jack of all trades; master of none." Some forms of "real" Tarot reading portray the whole deck (or at least the picture cards) as representing The Fool's journey to enlightenment.
In Toon: The Cartoon Roleplaying Game, characters can make a Smarts check to decide whether or not they can undertake a clearly impossible action. If they fail, they are presumed to be able to do it. This is one of the few examples from a tabletop role playing game where it's worthwhile failing a simple stat check.