Old Dog

Exactly What It Says on the Tin — an old dog, typically seen more often in a rural setting. It is frequently male, often will be some sort of hound, and usually splits its time between sleeping and barking. Sometimes known for having been a good tracker or hunter in the past.

In talking-animal fiction, the Old Dog may be portrayed as a grandfatherly character, or just as a crabby old guy.

On a more cynical note, old dogs are legendarily unable to learn new tricks. However, plenty of owners will dispute that and call it a wives' tale.

The dog's death (apparent or real) can be a Tear Jerker.

Examples of Old Dog include:

Film

Trusty in Disney's Lady and the Tramp.
Chief in Disney's The Fox and the Hound (film) fits the "crabby old guy" category.
Wylie Burp in An American Tail: Fievel Goes West, the old canine sheriff and a caricature of Wyatt Earp.
Shadow in Homeward Bound is a character of the grandfatherly sort.
In Air Buddies, the local police dog is a bloodhound called Deputy Sniffer.
The first dog to expire in Eight Below is an aging male who is too weak, and/or too loyal, to break loose from their tie-down chains.

Literature

Older Than Feudalism: Odysseus' dog Argos (20+ years old) is the first one to recognize his master (even in disguise) when Odysseus returns home at the end of The Odyssey. The ancient animal then finally slips its leash on life in front of him.
Candy's dog in Of Mice and Men is one-half to three-quarters dead from old age.
In the Savannah Reid mysteries, Savannah's grandmother has Colonel Beauregard. Though he spends most of his time sleeping, he did manage to take a bite out of the perpetrator of Peaches and Screams.
In the Warrior Cats graphic novel The Rise of Scourge, a dog named Samwise is sleeping in an alley. He loses a tooth... and that tooth helps Tiny become Scourge.
In stark contrast to the Disney example, Copper is the Old Dog in Daniel P. Mannix's The Fox and The Hound.

Music

Easton Corbin's "I'm a Little More Country Than That".

Picture a small town / with an old hound / Laying out front / of the court house...

The song "Old Dogs" by Bill Staines.

Old dogs have a song to sing, old dogs like most everything, fear not what the weather brings, except when it is thunder.
When their time on Earth is through, old dogs are forever true; around the bend they wait for you, come some tomorrow morning.

Walter Brennan's "Life Gets Tedious, Don't It?":

Hound dog's howling so forlorn
Laziest dawg that ever was born
He's howlin' 'cause he's settin' on a thorn
Just too tired to move over

Live-Action TV

The MythBusters busted the "old dogs can't learn new tricks" myth. They can, you just have to be more patient with them.
A staple on the comedy-variety show Hee Haw was an old hound dog that mostly slept on a front porch (played by four dogs through the course of the series).
The dog playing Buck on Married... with Children performed until he started having problems getting around. He was retired/"reincarnated" in a younger dog.
Mr. Dean's dog Bob in All Creatures Great and Small.

Newspaper Comics

In a Garfield strip, he meets an old dog next to a sign that says, "Beware of the Old Dog". "What are you going to do, gum me?" he snarks to it. He finds out quickly that "the old geezer is lethal with a cane..."

Web Original

In Peanuts Revival, a series of anime/manga-style drawings showing the Peanuts gang as teenagers created by an artist going by "gNAW" circa 2006-2007, this is one of the two options he plays with for portraying Snoopy, as seen in the last image on this page (which also can be found here).

Western Animation

Subverted in an episode of King of the Hill. Peggy gets a job working for the Alamo Beer Company and becomes privy to many of the company secrets. One of those secrets is that the supposedly old dog that appears in the Alamo Beer commercials is actually the third or fourth replacement and that the original dog died several years ago.
- Hank's dog, Ladybird, is also an example. She's a few months older than Bobby, which makes her over 65 in dog years.
In Family Guy, there's Herbert's dog, whose hind legs don't work.
In the very first episode of American Dad, Stan gives in to Steve's requests for a pet dog and adopts Thor, who clocks in at a positively ancient 19. Stan meant well; he thought Thor was better for having lived through the Reagan years, but as you can imagine the poor thing died very quickly.