After Bilbo's departure from the Shire, he leaves Adelard an umbrella as a gift: "Adelard had carried off many unlabelled ones" (1.1.130).
An uncle of Sam's; he appears when Sam comments, "Live and learn! As my gaffer used to say. Though he was thinking of gardening, not of roosting like a bird, nor of trying to walk like a spider. Not even my uncle Andy ever did a trick like that!" (2.6.116).
The most recent war that has been fought in the borders of the Shire (before the events of the Lord of the Rings series) was an invasion of Orcs fought back by Bandobras Took. This battle was a very long time ago (outside of living memory, says the narrator), which tells you how peaceful the Shire generally is. (Incidentally, this is the same Took whom Tolkien calls "Bullroarer" in The Hobbit – supposedly, he was strong enough to strike the head of the leader of the Orcs [Golfimbul] clean off and into a rabbit hole. And that, Tolkien tells us, is the origin of the game of golf. Neat!)
At Bilbo's birthday party in the first chapter, all of these fine representatives of the Shire families appear to help him celebrate. These are their names: a directory of Hobbiton society.
The Gaffer's next-door neighbor, with deep suspicions of Hobbits who live across the Brandywine River on the way to Bree (i.e., the Brandybuck family).
This farmer's land lies beyond Hobbiton, close to Bucklebury Ferry in Marish (in other words, in the Shire, but not in the same part of the Shire that Frodo and Sam live). Frodo, Sam, and Pippin stumble upon his farm as they travel off the road to the Brandywine River. Frodo is a bit shy of Farmer Maggot because, when he was a child living in Buckland, the farmer chased Frodo away from his mushrooms with his dogs.
But now that Frodo's all grown up, the farmer turns out to be helpful: like the Gaffer, he had a visit from a Black Rider looking for information about Frodo Baggins. Farmer Maggot refused to tell the Black Rider anything and sent him on his way. Farmer Maggot speculates to Frodo that this Rider is after some treasure of Bilbo's. Frodo won't (or can't?) answer, and Farmer Maggot doesn't pry. He does offer to give Frodo, Sam, and Pippin a ride to the Ferry in his wagon. Still, he hasn't forgotten that Frodo was once the child who stole his mushrooms: he recalls that Frodo was once one of the worst rascals in Buckland.
One of the younger generations of Hobbits who grew up with Bilbo's stories of far-off places; also a good friend of Frodo's. He helps Frodo pack up Bag End just before he leaves for Rivendell with Sam.
Many years ago, Gorhendad Oldbuck, head of one of the oldest families in the Shire, crossed the Brandywine River to the east and built Brandy Hall. He changed his name to Brandybuck and "settled down to become master of what was virtually a small independent country" (1.5.4). Brandy Hall is now a giant network of tunnels, and the people living there are in some ways quite different from those of the old Shire. They like swimming in the Brandywine River, and they are also a little more connected with the larger world.
The gardener at Bag End who preceded the current gardener, Ham Gamgee (the Gaffer).
Hugo Bracegirdle likes to borrow Bilbo's books and is careless about returning them. Pointedly, when Bilbo leaves the Shire, he gives Hugo a gift of an empty bookcase.
In an inversion of his gift to Dora Baggins, Bilbo leaves Milo Burrows "a gold pen and ink-bottle" (1.1.138), since Milo never answers letters.
These two examples of the Fallohide kind of Hobbit (tall and vaguely Elf-y) led their people west across the Baranduin River with permission from the high king at Fornost, in order to found the Shire. Since this time, the Shire has been the primary residence of the Hobbit folk. (To clarify where the heck Fornost, Bree, and even the Shire are, check out this map.
Farmer Maggot's wife; when Farmer Maggot sets off with Frodo, Sam, and Pippin to give them a wagon ride to Bucklebury Ferry, she warns, "You be careful of yourself, Maggot! [...] Don't go arguing with any foreigners, and come straight back!" (1.4.102). Mrs. Maggot also remembers Frodo's mushroom stealing past: when Farmer Maggot drops the three Hobbits off at Bucklebury Ferry, he passes on a basket of mushrooms from his wife to Frodo, with her compliments.
This elderly Hobbit sticks his feet on the table as Bilbo starts his speech at his birthday party. Once Bilbo disappears, Odo removes his feet and stamps for emphasis, out of shock.
A Hobbit from Bywater, one of the many Hobbits gossiping with the Gaffer about Bilbo's upcoming party in the first chapter. He's the one who offers this rumor about Frodo's parents' drowning: "I've heard they went on the water after dinner in the moonlight [...] and it was Drogo's weight as sunk the boat" (1.1.14).
Rory Brandybuck is an old friend of Bilbo's. In return for his hospitality over the course of their friendship, Bilbo leaves Rory "a dozen bottles of Old Winyards, a strong red wine from the Southfarthing" (1.1.143). Rory is extremely grateful for this fine vintage.
Odo Proudfoot's grandson; the day after Bilbo's party and sudden disappearance, Sancho begins "an excavation in the larger pantry [of Bag End], where he thought there was an echo" (1.1.157). Apparently, all of the Shire thinks Bilbo lived with tunnels of gold – not true, but the legend inspires silly Hobbits like Sancho to look.
Sandyman is the miller for Hobbiton (by the way, a miller grinds grain into flour). He's a mean-spirited gossip. When the Gaffer is sitting at The Ivy Bush inn talking about Bilbo and the residents of Bag End, Sandyman suggests that perhaps Frodo's parents' drowning was a murder rather than an accident. The Gaffer scolds him, "There isn't no call to go talking of pushing and pulling" (1.1.17).
Ted Sandyman is Sandyman the miller's son. Many years after Bilbo's disappearance, he sits in The Green Dragon inn and argues with Sam the same way that his father the miller argued with Sam's father a decade before. Ted thinks that Bilbo's tales of Elves and dragons are all a load of bull. He sums up: "Oh they're both cracked [...] Leastaways old Bilbo was cracked, and Frodo's cracking" (1.2.29). Sam is outraged at his jibes.
Old Toby is the first grower of Hobbit pipe-weed on record; his area of the Shire (Southfarthing) is still known as the best producer of pipe-weed for smoking. Old Toby is also the name of an excellent kind of pipe weed.