Magic System: how many spells is enough?

When I’m gaming and I’ve got a magic user I like the concept that the character can, with enough time, make spell effects on the fly. Throughout almost all the inspirational fiction the magic user is not very limited in their magic variety: just their power. They can come up with something for most any situation. I like this. What bothers me is that in the RPG sense it needs to be codified and defined. Probably to keep rules lawyer/munchkin types in line.

What do you think of magic systems with a limited series of defined spells?

What if the magic system has a limited series of defined spells and a guide for making new ones as required?

In my experience most GM’s will make up new spells without batting an eyelid – every time a new magic item comes about a new spell has to also come about to make said item.

I’m very interested in people’s thoughts on magic system ‘enumeration’.

Magic System: how many spells is enough?