Not enough to show, unless you are being comic and having the characters know they are in a game world. Enough so that the readers won't protest that the wizards and clerics can't possibly be out of spells after so little use of them.
But then there are sliding skills. A thief is a master at climbing, picking locks and disabling traps, and persuasion. His level will determine his proficiency but since he's not going to talk about what he rolled, the precise level is unimportant. Beyond perhaps some suggestion that he's the master of some trades because he's not the jack of all.
Or a ranger's tracking, fighting, and wilderness survival skills. Getting the party to survive a raging windstorm, or tracking down the wolf, is something he doesn't measure out in spells cast.
Gaining a level is more interesting still -- going to have to have people commenting. Though not so interesting as a sorcerer gaining a level. How does a sorcerer know, "O, I got a new spell and this is how I cast it"?