Answer:
It all depends on your taste in music.
If you like the pop-rock genre then I strongly reccomend the All-American Rejects, as they are very popular with songs like "Move Along" and "Dirty Little Secret" and "It Ends Tonight".
If you prefer an electronica-dance type then Daft Punk is a wonderful choice. They created some old, but widely known songs like "Harder, Better, Faster, Stronger" and "One More Time".
If you enjoy rock music, then you should love bands like Aerosmith and The Rolling Stones. They may be old, but their music lives on.
As for hip-hop groups, I'm not very knowledgeable with this category, but the Black-Eyed Peas have a good electronic hip-hop sound. I don't exactly know what genre the Pussycat Dolls are, but I'm pretty sure it's somewhere along the lines of hip-hop.
Rap artists seem to prefer working alone rather than in groups. I recommend Eminem and 50 Cent. I would also recommend Soulja Boy, but it seems that I'm the only one who will listen to his music nowadays.
As for other music genres, I'm afraid you'll have to wait for somebody else to answer, but I hope that this helped. =]