My wife is an alien resident with H4 visa. She is not allowed to work in US but does some professional work and receives dividends in our home country. Does she have to declare her global world income in the US?

Yes, on the return, you must both report your worldwide income. Another filing requirement may be Form TD F 90-22.1. Your U.S. Tax Return: U.S. Citizen or Resident with Foreign Income (http://taxipay.blogspot.com/2008/03/us-citizen-or-resident-with-foreign.html)

Yes, she needs to include all income on her U.S. tax return. If she owns more than 10% of any foreign entity she may need to file Form 5471. If she owns any foreign mutual funds, she may need to file Form 8621.