Jeremy 'Dreamy McMug' Meeks -- A REALLY Bad Dude

Jeremy Meeks -- aka Dreamy McMug Shot -- is a BAD GUY ... that's certainly what his rap sheet shows.

Meeks -- who has owned the Internet the last few days with his perfectly lit, eye-gazing mug shot -- has been in and out of prison for more than a decade.

The 30-year-old was charged in 2002 with robbery and corporal injury to a child. He allegedly jumped a 16-year-old and beat him to a pulp. Meeks copped a plea and was sentenced to 2 years in a California prison.

According to docs, Meeks admitted during the case he was affiliated with a criminal street gang, which is a felony in California. The docs say he was a Northside Gangster Crip.

Meeks served his time and moved to the Spokane area of Washington, and in 2007, he was charged with identity theft and resisting arrest. According to legal docs ... he was in a sporting goods store and tried to steal a package of pellets and when security guards saw him, Meeks screamed, "I'll f*** you all up." The guards peppered sprayed Meeks into submission. He was convicted and served time.