Are the Ability Score Increases that are received at character levels 4, 8, 12, 16, and 20 untyped bonuses? Or, are they typed? If so, what type of bonus are they?
I vaguely remember them being typed in 3.5, but I don't remember what type they were or if the typing carried over.
I also think I remember there being a limit to no more than 5 such bonuses to a single ability score. Is this still true in Pathfinder?
They are untyped, they were also untyped in 3 and 3.5 - at least according to my hardcopies.
I suspect you may be thinking of the various tomes and wishes which provide inherent bonuses, which are limited to +5.
The ability score increases for level are untyped bonuses and stack with any other bonus, including themselves. Thus, you could put all five into one score.
Wish and similar magic that increases ability scores, such as magical tomes, have a type. They grant an inherent bonus to ability scores, and thus do not stack (unless the wishes are used in rapid succession - this is an exception to the standard rule.) Inherent bonuses are capped at +5.
The text of Wish reads: "Grant a creature a +1 inherent bonus to an ability score. Two to five wish spells cast in immediate succession can grant a creature a +2 to +5 inherent bonus to an ability score (two wishes for a +2 inherent bonus, three wishes for a +3 inherent bonus, and so on). Inherent bonuses are instantaneous, so they cannot be dispelled. Note: An inherent bonus may not exceed +5 for a single ability score, and inherent bonuses to a particular ability score do not stack, so only the best one applies."
The text of FAQ stats: "According to Table: Character Advancement and Level-Dependent Bonuses, a character gains an ability score increase at level 4, 8, 12, 16, and 20. How much is this increase? What ability scores does it affect?
At 4th level, a character can increase one ability score by +1. This is a typeless, nonmagical bonus that cannot be changed once selected.
For example, a fighter with Dex 13 could use this bonus to increase his Dex to 14.
A character can also increase one ability score at 8th, 12th, 16th, and 20th level; it does not have to be the same ability score as the one chosen at an earlier level, and stacks with all other bonuses.
For example, the aforementioned fighter could use the 8th-level bonus to increase his Strength from 15 to 16, then use his 12th-level bonus to increase his Dex from 14 to 15, and so on."
The largest enhancement bonuses (belts, headbands and such) in published materials are +6.
The largest inherent bonuses (manuals, tomes, and just wishing in a row) are +5.
While not on items, there are larger enhancement bonuses available. There isn't an actual cap on it, the items just to tend stop at +6. And as no one ever brought up enhancement bonuses or a cap on them, I don't see why that is relevant anyway.
While there is a cap on how much inherent bonus wishing can get you, there is no cap on inherent bonuses per se, certainly not 5.
Strength of the Abyss (Ex): At 9th level, you gain a +2 inherent bonus to your Strength. This bonus increases to +4 at 13th level, and to +6 at 17th level.