The Tramp

The Tramp is a vagrant. He rarely has any material possessions. He survives from day to day via grifting and playing off others' sympathies, although the more principled ones will be eager to take what honest paying work he can get. He's usually quite intelligent, though, and is careful not to do anything truly horrible. He is often Chaotic Good.

If the heroes are looking for a down-to-Earth character to restore their faith in humanity, the Tramp can usually do it. He's also well-connected, though it's usually with other tramps; they form something of a cooperative union.

In some works, the existence of the Tramp can be proof of a Crapsack World.

Tramps are sometimes portrayed as straight villains, but this role usually falls to Crazy Homeless People in modern fiction.

The Tramp is most common in works Older Than Television. Between improvements in the social net and anti-vagrancy laws, real tramps have been displaced for the most part; sane people just don't live that way anymore. Tramps still turn up in period pieces, though.

Tramps are often portrayed as Walking the Earth (that's almost part of the definition) or being Closer to Earth.

Tramps are a sub-class of Hobos.

Examples of The Tramp include:

Anime and Manga

The Tokyo Godfathers.
Played on in the English title of Kimi wa Petto: Tramps Like Us. Momo, the male lead, is practically homeless, sleeping on couches. Our female lead, Sumire, finds him sleeping in a box.

Film

Most of the characters portrayed by Charlie Chaplin fall under this type (and, in fact, "the Tramp" is often the closest thing the character has to a name - Chaplin's Tramp may well be the Trope Namer). Before Hilarity Ensues, the Chaplin character can often be found trying to think of a way to get dinner.
The Tramp character of Walt Disney's Lady and the Tramp. Although he is, admittedly, a dog.
Both versions of My Man Godfrey, though the forgotten man aka tramp started out rich, goes on to be a tramp, makes the money back and uses it to help the other tramps. Oh, and marries the pretty rich girl.
The title character in Aladdin is like this, a tramp and beggar living on the streets off his own wit and what he can con/steal; until he gets the lamp, at least.

Literature

Pretty much everyone at the Court of Miracles in The Hunchback of Notre Dame. In fact, Gringoire becomes a tramp once he gets there on penalty of death. Later in the book Jehan joins up, too, mostly because he's run out of money and is tired of going to school.
The Astrid Lindgren book Rasmus and the Tramp (also known as Rasmus and the Vagabond)
A Vagabond Journey Around the World features Harry Franck in his voyage to make a trip around the world without spending any money. He inevitably falls into the character type, as do most of the other people he befriends.
In Gene Stratton Porter's Freckles, what he looks like at first appearance:

At a glance he might have been mistaken for a tramp, but he was truly seeking work.

Ben from The Borribles trilogy is a smelly, dirty bum who befriends the Adventurers, and provides them with both shelter and a useful contact in the form of Knibbs, a friend who is a drayman. Unlike most tramps he has a permanent home -- a shack built of scrap wood and metal on the mudflats of the Thames -- and occasionally he works as a drayman with Knibbs.

Live Action TV

Freddy the Freeloader, one of Red Skelton's alter-egos.