Just last week Microlite74 was released. It's a d20 variant designed to have modern rules (based on Microlite20) that enable an old-school play experience. It manages to get character creation, task resolution, spells, and more than 80 monsters into a mere 4 pages!
But my purpose in posting is to quote this paragraph on skills in the game. It really highlights the old-school philosophy of success being a matter of thinking, rather than dicing:
Unlike most modern RPGs, there aren’t any skills. Players are intended to have their characters act like adventurers. So don’t search your character sheet for the perfect solution in Microlite74. Instead, you just tell the GM what your character is trying to do. If you need to keep a door open or shut, tell the GM your character is using a spike to keep the door open or closed. A ten foot pole is your friend for checking for traps. Searching a room means looking in and under objects, not rolling a skill check. While this may seem strange at first, you will quickly learn to appreciate the freedom it gives you. No longer are you limited to the skills and feats on your character sheet, you can try anything your character should be capable of trying. You might not succeed, but the rules generally will not stop you from trying.
I'm not completely opposed to skills in RPGs, though. Having skills in an exploration-focused RPG system is good for one thing: indicating something about the character you're playing. What they're not good for is mechanically framing a fictional interaction that is, in its basest form, a creative exercise. Heavily mechanised skills encourage players to seek the "right" answer to an in-game challenge instead of applying their imagination. And, after all, isn't the point of playing an RPG to be creative and imaginative?