To adhere strongly to, to follow closely. Also used to describe the presence of an unwanted person who will not take a hint.
1) That adhesive is brilliant. It sticks like shit to a blanket!
2) I knew they were following me, but I couldn't shake them off. They stuck to me like shit to a blanket.
3) She latched on to me in the bar and I couldn't get rid of her. She stuck like shit to a blanket.