Varsovian:
One note: rules for spells *are* intimidating. For instance, clerics have normal spells, orisons, domain spells, domain powers... I feel like a player might need a flipchart to organize all this.
The multiplicity of spells generally doesn't provide too much of a burden, and as the spellcaster is usually one of the classes that requires a bit more bookkeeping in nearly any system, I hope the player in question would be prepared to write things down.
I've played both arcane and divine spellcasters, and I will say that a domain spell, as it is generally used by divine casters who prepare their spells, effectively just becomes another part of your daily prepared spells. It's actually easiest to remember, as that one spell slot rarely changes.
Orison and cantrips are also not too bad. They are either low-level divinations (detect magic, detect poison) that are busted out in non-combat situations, minor combat spells broken out in extremis (ray of frost, acid splash, spark), or small utility spells (mage hand, open/close, prestidigitation). No one has very many at any one time (the max is 6), and because they are so minor, they aren't going to tip game balance very hard one way or the other.
Special powers, like domain powers, bloodline powers, school powers, oracle powers, witch curses, etc., those are class features. I jolly well hope you remember your class features. Like your spells and weapons, these are the things you look at when determining your options for actions in any given situation.
All of this does require more tracking and writing than, say, your average rogue, but anyone who wants to jump into a spellcasting character should be ready with their pencil. I don't think it's excessive, and once you know roughly what spells you're going to have for a given situation, you just use that list for the adventuring day.