For example, Ur-Priest gains the next level of spell at every class level (instead of every other class level, like cleric). Are there any other classes (of any type) that get higher-level spells more quickly like this?
There is a very short list of full, accelerated casters:
- Ur Priest - like a Cleric, but in 10 levels
- Beholder Mage - like a wizard in ten levels that also breaks the action economy
- Blighter - Druid spellcasting in 10 levels, but off a much smaller, eviler list
- Apostle of Peace 1-9 in 10 levels; technically playable; wrecks parties. Casts off a short list of “good” themed spells.
- Divine Crusader casts off a single domain list (only), but gets them all in 10 levels.
As @KRyan noted in comments, most of these classes go 10 levels, but hit 9th level spells at the 9th class level (which is a title case Big Deal — 9th level spells are a quantum leap in power)
There are also a couple that start with higher level spells:
- Sublime Chord - combination of bard and wizard, 4th-9th level spells in 10 levels
- Nar Demonbinder - a small, broken spell list going 4th-8th in 7 levels.