1. No Skills
Searchers of the Unknown is an example of this. There is no codified mechanic for determining if a character successfully performs a particular skilled action. That said, the DM and players can still improvise a method: "Well you said your character used to be a blacksmith, so you have a 40% chance of crafting a magic sword that shoots laser beams."
Classic DnD uses class to determine the training characters have. So a magic user could be considered skilled at making potions, etc. There is also the possibility of using the same approach as in the "No Skills" system above for activities not covered by character class.
DCC, puts an interesting twist on this. In addition to an Adventuring Class, characters have an Occupation(basically a non-adventuring class) which they practised before they began adventuring. As such, the character is considered skilled in any skill that the occupation would cover. Skill checks for a character with a relevant Occupation are made as a 1d20+Ability Bonus(-3...+3) vs. the DC, a number reflecting the difficulty of the activity. Characters without the relevant Occupation may also try, rolling a d10 in place of a d20.
3. Skill Level
DnD 3.5 allowed characters to acquire skills, independent of any class or ability score. Skill checks are rolled as a 1d20 + Skill Level(maximum 3+class level) versus the skill difficulty.
4. Ability + Skill LevelWFRP 1st Edition does this. Basically skills can give a bonus on your ability check. The downside is that each skill has it's own rules for doing this, which means a lot of page-flipping/memorization.
Stars Without Number allows you to become trained in skill with a level of between 0 and 4. The skill check is then performed as 2d6+Skill(0-4)+ability modifier(-2..+2) vs. a difficulty number of about 6-13. Except combat which is d20-based.
Cyberpunk 2020 has something similar. Ability scores are between 1 and 10, as are skill levels. So a skill check is made as 1d10+ Skill+Ability vs. a difficulty number between 1 and 30. Of course, CP2020 takes the skill system a step further, making it the unified mechanic for all actions including combat, rather than a secondary system to the main combat mechanic as in DnD and WFRP.
The System for You
Anyway, so what system to pick for your game? Well, skill systems add a complexity to character creation and the game in general. So my personal preference is to have the simplest skill system I can get away with. For medieval technology-level games, I don't think a skill system adds much. For my Pirate game, that's DCC Occupations. For a modern or futuristic game, I'm more likely to prefer some variant of Ability + Skill Level.