I like LotFP's simplicity but there's one thing I am not so sure about. Character abilities don't affect skill success propablities. No matter how dextrous you are you are as good in Sleigh of hand that the next guy.
This is a small modification if you want abilities to affect skills.
You can re-roll skill roll as many times as you have ability modifiers for a related ability but the minimum of skill rolls is always one.
For example if your character uses Sleigh of hand and your DEX modifier is +2 you get to roll the skill roll twice and pick the better result. If DEX modifier was -1 to -3 you only roll once.