Well The Hobbit is pretty much a prequel to LOTR in the same era and world, in Middle-earth. So pretty much all locations and characters are connected one way or another.
The one Ring, introduced in the hobbit, acts as the major plot device in LOTR. The Hobbit tells the tale of how Bilbo came into possession of the Ring. This is the basis for the entire LOTR trilogy.
Frodo, the main character in Lord of the Rings, is his nephew and heir. He inherited the Ring from Bilbo.
Gimli in the fellowship of the ring is the son of Gloin. Gloin is a member of the dwarves in league with Thorin Oakshield in the quest for mount Erebor.
Thorin Oakshield was the son of Thrain II, who had the last of the dwarven rings of power which was taken from him in Dol Guldur by Sauron. His father Thror was slain by the orc Azog. We meet Azog’s son Bolg as a chieftain of the orcs in the battle of the five armies.
Dain Ironfoot, who ruled mount Erebor after the battle of the Five Armies, was still alive in LOTR, where he fought off the invade of orcs in the Battle of Dale alongside the men of Dale including Brand.
Balin, another member of Thorin’s party, and Bibo’s best dwarven friend, is the same Balin who’s tomb was found in the mines of Moria by the fellowship. He took a host of dwarves from Erebor to Moria to try and reclaim Moria but failed.
King Thranduil is the father of Legolas.
As far as events goes, the most notable one is where Gandalf left the party just before Mirkwood. In LOTR we learn that he’s attending the white council to drive Sauron away from Dol Guldur.
Also there are some objects like Ocrist and Glamdring. In the hobbit we read how Gandalf came into possession of his sword Glamdring. Also Bilbo’s sword Sting earns his name in The Hobbit. He passes on the sword to Frodo in Rivendell along with his mithril vest, which he found in Smaug’s treasure pile.