I'm assuming you have in fact read Harry Potter - if not, for whatever reason, they genuinely are good. Admittedly the first two books are very much children's books, but starting with book three they rapidly become less so, and Rowling is quite good at subtle plotting, using elements from several books ago that didn't seem important at the time, so even the first two books aren't as simple as they seem.

Jacqueline Carey's Kushiel series consists of a pair of trilogies, and now some more books, so that should make it long enough to qualify. The first trilogy is far superior to what follows, I'd recommend that. A good amount of sex (the heroine has strong masochistic inclinations, which doesn't stop her from being quite effective as an agent on various missions and adventures), don't know if that might bother you. The setting is some kind of alternate history medieval France/Europe, it's quite interestingly done, lots of subversions of actual medieval Europe/Middle East. That plus the excellent heroine and quite good plotting makes the first trilogy among my favourite fantasy series; unfortunately the protagonists of the later books aren't as interesting.

You're also missing everything by Tad Williams, who is on his fourth series now, I think, each of them in a totally separate universe, generally tetralogies. Memory, Sorrow and Thorn is a pretty good fantasy series, while Otherland is superb near-future SF (with a liberal dose of fantasy - most of the series is set in a number of different virtual realities, running the gamut from Middle Earth over Mars and Ancient Egypt to the Troy of the Iliad).

Then Janny Wurts, I know my fellow admin Rebekah is a great fan of her magnum opus The Wars of Light and Shadow, which must be close to a dozen books by now (haven't read it myself). She also co-wrote an interesting trilogy with Feist and another one on her own (I read both, but the latter doesn't seem to have left much of an impression), but I suppose by your rules trilogies aren't allowed.

Another one that I haven't read myself, Narnia by C.S. Lewis, I'm not quite sure whether I really should read that...