How many skills should a 15th level character have at 10+, 15+, 20+?
I don't have a great sense. Besides, it's going to vary depending upon the campaign type whether to concentrate or to diversify. In our games, athletic and knowledge skills are extremely important, which forces PCs to go for breadth and to take more esoteric skills than the usual "adventurer skills" (Spot, Search, Tumble, Heal, ...) that some people might concentrate in.
Average DCs should go up over time to maintain the challenge level. New characters should usually be faced with DCs in the 10-15 range with something very difficult being 20. At 15th level, I'd expect the most common challenging DC to be 25 with 20 being something expected to make and 30 being very difficult. Obviously, opposed rolls become harder when facing higher level adversaries.
Not that the challenges should remain the same. A low level character may be climbing a tree where a high level character may be climbing an ice wall to achieve the same purpose in the adventure.
Skills are not made all alike. You don't need everyone in the party to be knowledgeable about religion, but it helps for everybody to be able to climb. In general, higher level characters should need to diversify to handle a wider range of challenges.
I believe a lot of reasonably built PCs can get by okay with a long skill list, but there are strong disincentives to putting ranks into esoteric or flavorful skills. That's a problem to me as it makes characters look alike and I usually am on the side of character diversity.
For what it's worth, my 14th level character has 13 skills at 10+, 3 at 15+, and 1 at 20+. That's quite different from treeplanter's character (from the other thread) that has 5 at 15+ and 2 at 20+ as a 12th level character.
Actually, here's a pretty good example of differing priorities with these two characters. Mine is also an archer and has a Craft: Bowyer bonus of 10, where his character appears to put no ranks in it, for a bonus of 3. Is C:B useful? Until recently, it was pretty much irrelevant. I recall making a roll like once. Still, the genre should support the idea that weapons need to be replaced on the fly. I do feel like I've found a way to make the skill useful by having custom designs be gifts, so I'm not annoyed by sinking ranks in it. And, of course, such a character should have this skill at a decent level. I'm not as thrilled, though, when having to make swim checks with a bonus of 3 or search checks with a bonus of 4 because I'm stretched far too thin.
Put another way, it's a strawman argument to believe anyone wants characters to have 18 ranks in everything or even just be +18 at everything. There are always going to be skills that characters suck at unless you remove most of the skills in the game; if they never matter, then they don't need to exist, if they do matter, then the character is not going to be competent at everything. Now, some level of sucktactitude helps make RPGs work better as it justifies being part of a party, a team. OTOH, this isn't D&D where parties are supposed to be designed as interlocking puzzles of specific skill sets with magic solving everything. Being reasonably competent at a lot of different skills makes more sense to me thematically, just as your typical fantasy protagonist is skilled in numerous areas.
