As I'm sure nearly everyone who reads this blog knows, I'm not a big fan of adding skills to D&D, which I think works just fine without them. This is partly due to my understanding of character classes and partly due to the fact that D&D already includes a number of mechanical systems that handle most of the skills needed by adventurers. In my Dwimmermount campaign, I've simply formalized the systems present in OD&D and added one (climbing) that seemed to make sense, though its use actual use in play has been very limited.
Break Locks: Dwarves, elves, and Men can break open a lock on a roll of 1–2 on 1d6, while gnomes and goblins can do so on a roll of 1. This roll can be modified by Strength. Note that locks opened this way are broken, not picked, which makes a loud noise, particularly when applied to locks on doors, and may alert nearby monsters of the character's presence.
Climb: All characters can climb sheer surfaces on a roll equal to or under their Dexterity score on 1d20, if they have rope and a grappling hook to aid them. Only thieves can do so without such aids. Likewise, the referee should apply penalties to particularly difficult climbs or when conditions make the ascent unusually hard.
Find Traps: Elves, goblins, and Men can find non-magical traps by actively searching on a roll of 1 on 1d6, while dwarves and gnomes can find them on a roll of 1–2.
Listen: Men can hear sounds from behind a door on a roll of 1 on 1d6, while nonhuman characters hear them on a roll of 1–2.
Observation: If actively searching, non-elves discover secret doors and other hidden features on a roll of 1–2 on 1d6, while elves discover them on a roll of 1–4. However, if elves pass within 10' of a secret door or hidden feature, there is a 2 in 6 chance they take notice, even when they are not actively searching.