Three of the men convicted by the criminal court on Tuesday are Kuwaiti nationals, while the other three are bidoons, persons without nationality.
A seventh accused, a Kuwaiti, was sentenced to life in prison.
The condemned are members of a group linked to al-Qaida calling itself the Peninsula Lions Brigades.
The six were among 37 others charged with links to groups in neighbouring Iraq and Saudi Arabia.
The court, however, acquitted Usama Minawir, a lawyer for Islamist groups in Kuwait, and Hamid Abdullah, a former leader of Salafi groups, according to Aljazeera's correspondent.
Police said some had confessed to planning attacks against US military and Western targets in Kuwait.
A Reuters reporter said some of the other suspects received jail terms of between four months to 15 years, one received a life term, and seven were acquitted.
Prosecutors had demanded the death penalty for about 20 suspects for four shootouts in January in which nine of these men and four security personnel were killed.
Eleven of the 37 suspects remain at large.
Used as the main launch pad for the 2003 war in Iraq, Kuwait hosts up to 30,000 US troops and is the main transit route into Iraq. About 13,000 US citizens live in Kuwait.