Perk Rate is a derived statistic. It affects how often the character is allowed to pick a perk. A character's perk rate depends on his race and on certain traits such as Skilled (which increases the rate) or Fear the Reaper (which decreases it). Some perks, like Divine Favor, may decrease the perk rate as well.
Fallout and Fallout 2
In Fallout and Fallout 2, the perk rate is 3, which means that it is possible to pick a new perk every 3 levels. You are not able to save up perks to use at future perk acquiring levels. Any unselected perk will be lost forever at the next perk level if you do not select one before this time. E.g. level 3 > perk not chosen, level 6 > perk not chosen (level 3 perk point lost), level 9 > better criticals chosen (level 6 perk point lost).
Fallout 3 and Fallout 4
In Fallout 3 and Fallout 4, the perk rate is always 1 - that is, you can pick a new perk every level. Also in Fallout 4, a perk point is not lost if it is not spent before the next level. They can be banked indefinitely.
Fallout: New Vegas
In Fallout: New Vegas, the perk rate is set at 2 - You get a new perk every two levels. As in Fallout 3, perks cannot be saved for later use; they must be chosen the moment the player character is out of combat.
In Fallout Tactics, the racial perk rate for humans is 3, which means that they can pick a new perk every 3 levels. The rate is 4 for ghouls, super mutants and deathclaws, and 2 for dogs. Robots cannot pick perks at all, i.e. their perk rate is infinity. You are able to save up perks to use at a later time.
Fallout: Brotherhood of Steel
In Fallout: Brotherhood of Steel, "skills" work like perks in other Fallout games. The "perk" rate is 1.