This can only be done once per day no matter how many different kinds of class-appropriate challenges come up that day.
The maximum is + 1o. (10 total including ability score bonuses, if you're using a DC system). After 10 you get to do it twice a day and split the bonus numbers however you want.
Scruffy The Bandit and Muppet the Sorceress want to try to interpret the hieroglyphs in a dusty old codex. Scruffy has to roll an Int check (at -8 or at a DC of 18, because the DM says so). Muppet also has to roll an int check (also at -8 or at a DC of 18, because the DM says so) however, Muppet may choose to call on her vast sorceressy training to do this and thus can add +5 since she is level 5.
If, later that day, they come upon an obscure alchemical substance, Muppet is out of luck and has to roll like everybody else, as she's used up her training bonus for the day.
If she was level 13, she could add 5 and bank 8 for later that day or add 10 and bank 3, or whatever, up to 10.
-If you are including thief functions in this, thieves do it all the time--not just once per day--up to +10 total (including any ability score bonuses, if you're using the DC system). Edit: In an old-school system, this means the standard array of thief abilities tops out at +10, so this requires a further hack--maybe at this point the thief starts being able to dip his or hands into other classes' skill pools. Like how they can start to read magic or whatever at a certain point...
-If you want to use it with a whole skill system, then just modify the rule so it says "Once per day a PC may add his/her level to any single ability check involving a skill s/he has"
...and otherwise skills don't do anything.
-This whole system probably doesn't apply to saving throws. But consult your GM
Um, Dude, Why Bother?
I like this system because it creates a situation where tasks that challenge a high-skill PC do not have to be completely out of the range of possibility for low-skill PCs.
It compresses the difficulty scale, essentially.
The high-level adventure does not have to be full of tasks that only one possible class (ranger, thief, druid) could possibly do right.
So you can make a wall at, say, climb check= dex - 4. A fighter might have trouble climbing that wall, but they could make it. A thief of any level could also have trouble climbing that wall, but their level would still matter if they wanted it to.
Or you could make tracking a foe through a marsh check at simply -1 int. The ranger does not have to have a high int to successfully follow the tracks and be better than other people at it, but anybody else still has a shot to follow them. Because, hey, it's tracks in the mud.