I should have a list of links I can just cut and paste whenever someone asks this question, we seem to see it once a week.

Not that it isn't interesting to talk about.
To make D&D entirely skill based, including BAB, BDB, magic-using, plus all the things that are already considered skills, you'd end up changing it so much that it wouldn't be recognizable as D&D. It's not impossible, but it's a lot of work. Plus, you'd just be re-inventing the wheel, there are already skill-based systems out there. If you really want one, use it.
Problems: For instance, BAB would be a super-skill. Characters would max it out all the time. And why wouldn't they? Say you have one combat and one skill-challenge in a night (climbing a wall or whatever). In that one combat, you're going to roll to hit at least once a round for the 10 rounds or so the combat takes. You'll roll climb once or twice, total. Your other skills (jump, swim, open locks) wouldn't be used at all. Strictly on a per-use basis, BAB is the best use of a PC's skill points. To make it more balanced with other skills, you'd need to divide it up into something like swung weapons, thrusting weapons, pole weapons, or however else you divided it.
Plus, it would start at +4, instead of +1, so people would hit much more at lower levels. You'd have to adjust enemy ACs or hit points to compensate. Or you could max out skills at =level instead of level+3, but then a DC 15 challenge, normally considered appropriate for a 1st level character with that skill as a class skill, is really too hard for a 1st level character to be expected to succeed at regularly, so you have to scale down the DCs of normal checks. Or else 1st level characters become incompetant boobs, and that's not real fun to play.
And skill-based magic? Fuggetaboutit. You can't retain the feel of D&D magic with a skill-based system. It's hard to even get a work-similar, let alone a work-alike. I worked on it for quite a while and couldn't get anything I was happy with.