I'm into wedding video business, however was puzzled by the copyright music issue. Do I have to pay or get a license for those music and songs I used in the video, and if yes, how should I do it. If there any way to go around it?

There's so many threads about this, a good place to start is the sticky thread entitled "Will I get caught?"

http://dvinfo.net/conf/showthread.php?t=49607

Then, I'd go searching the forums for threads on "copyrighted music" and "weddings". There's a bunch of great threads out there.

Although, if you're operating in Singapore, the laws may be slightly different. I have no idea.

The answer to your question is YES! 99.99999% of videographers don't. But they should.