The solution isn't to add skills, but to take them away
This! In my experience, the more skills a character has, the fewer things a player will try that aren't on his/her character's list. Since that is not a play-style I want to emphasize I have used (and am currently using in a modified game of basic) a different set of skills:
Each character has three skills.
The first is a background skill, called whatever the background is called. It provides a bonus to any ability check that a person with said background should reasonably get a bonus to. This skill, like the background, itself, is easily made up by the player at character generation and is intended to be a
very quick way to help the player differentiate the character from others of the same class.
The second skill is the class skill. A character is assumed to be skilled at being whatever class they are, so they get a bonus to ability checks that are related to that class, as well. This is the main utility-skill of the character, most likely to see use on a somewhat regular basis.
The third skill is a specialty. At character generation, I ask the players what one thing their characters are better at than anyone else they know. This one produces some interesting results, depending on what mindset the player is at when creating the character (for instance, a player once had his character specialize in "Luck"). As with the other two skills, all ability checks made that ought to be enhanced by the specialty get a bonus. This skill is intended to help the player distinguish the character as an individual (again, very quickly).
That's it. It's easy (especially for neophytes), encourages situational problem-solving, does
not encourage players to spend the whole session with their eyes on their character sheets, and helps speed up character generation.
'Course, this is all easy enough to house-rule over whatever skill system they come up with. So, even though I voted "No," my actual vote is "I don't care."