I think it was 2nd edition AD&D that introduced the world to the Use Rope skill. I'm not sure whether this list o' skills system idea grew out of the game organically or if it was bolted on because other systems were doing it, but it seemed like a good idea at the time. I thought it was cool that my Fighter was a good fisherman and mountaineer. I'm looking at it again now however, and I think that it's not been such a successful idea.
Initially you had class tables, stats and saving throws to give some base values to hang success checks off of. You wanted to try something use the table. If you had no table you would make a strength check, or make a saving throw. If you could replace those class tables, various stunt tables and saving throws with a set of skills maybe that would be better. However the skills didn't replace the old stuff, they were bolted onto the framework so now you had more moving parts. Also the skills didn't really integrate into the classes and they certainly didn't integrate into the level system very well. Add to this you will still have those cases where there is ambiguity and no skill to cover the situation so you are either stuck making new skills or new tables for these new solutions or calling for more stat checks or (sometimes arbitrary) saving throws based on the situations. How many modules had a one off weird effect that was save vs wands? Mixing list of skills with a class/level geared system can probably work, but it isn't going to be a graceful child.
That's why I like the Microlite skill system. The skills and the stats are integrated with the classes and level advancement and they are generic enough that when they are matched to a Stat they can apply to most situations. You don't need special saving throws because you can assign a skill or stat check to do the same function. The 4 Microlite Stats are STRength, DEXterity, MIND, and CHArisma. The 5 Skills are Physical, Subterfuge, Communication, Knowledge and Survival. It's a 4x5 grid system. By using them individually or mixing these up with the stat bonus applied to the Skill value you can assign a base number to most activities that aren't covered by (the few) denoted combat or magic rules. Also depending on how a task is described by the players you can assign a more appropriate base number.
Say your players want to leap a wide chasm - you can use Physical + STR bonus to see if they do it. The Rogue isn't happy with this due to a low STR stat, and describes using a sapling as pole to vault over it so you let her roll Phys+DEX instead. To convince the henchmen to follow them into a magic portal you can say Comm+CHA or MIND bonus depending on if they make a stirring oration or a reasoned plea. Pick a pocket - Sub+DEX, out lie a minstrel - Sub+Comm, hide a ferret in their pants... um perhaps Sub+STR? Use a friggin rope? Well that depends on what you use it for but however it is used you have a lot of options here including Sub+MIND (rope tricks), Phys+STR (climbing a rockface), Survival+MIND (making a snare loop), Comm+CHA (Well you get the idea).
The class bonuses to the Skills also reinforces the system, not only mechanically but by encouraging styles of problem solving. Fighters who are always working with their bodies are consequently utilizing their physical skills, Mages are going to be better at Knowledge based tasks, and Rogues get benefits from doing things the sneaky way.