There are so many! The two longest are Nipmuck an Natchaug. Nipmuck Trail goes from Mansfield Hollow State Park near UConn all the way to the MA border at Bigelow Hollow State Park. Natchaug Trail goes from Godwin State Park through Natchaug State Forest to Nipmuck Trail in Yale-Meyers Forest. There are tons of small local trails, many can be seen on openstreetmap.org.