SHINee!
I am just a fangirl! /squeal/ I actually got into K-POP because of Ring Ding Dong (the MV especially~) Their older songs and newer songs are great too (their debut song was Noona Neomu Yeoppo - the English name is Replay). A.Mi.Go, Lucifer, and Hello were great too. C:
To be honest, SHINee is probably the only boy group I REALLY follow, so I can't help you out with other boy groups that you haven't already listed/others haven't already listed.
CNBlue is alright as well, but they're more of a band. C: Search up their song "I'm a Loner"~ It's pretty catchy! :'D
Though I'm not crazy about them (never really looked into the group), many of my friends are fans of Big Bang. I'm pretty sure most of the members have had solo albums too (for example, G-Dragon's Heart Breaker was pretty catchy and Taeyang's Wedding Dress is absolutely amazing).
As for girl groups, I really like KARA, f(x), and Miss A in terms of the overall appeal (group members, personalities, songs, music "styles"). For KARA, Mister and Lupin (though some of my friends didn't like the music video) are pretty good. For f(x), I really liked their debut (La Cha Ta), Chu~, Nu ABO (which takes some getting used to), and Hot Summer (though it's a remake). Miss A is fairly new, but I've liked all of their songs so far (especially Bad Girl Good GirlGoodbye Baby).
and
SNSD is alright too (though, to be honest, I don't quite like some of their members), in terms of music and dancing. Gee (if you haven't heard it already), Genie, Run Devil Run, and Mr. Taxi are among my favourites from them.
A really great solo artist is IU (I liked her Good Day song~). Of course, BoA is amazing as well. C:
