Fry finds his old dog (fossilised) in a museum exhibit. It's done the same way as "Luck Of The Fryrish", with flashbacks intermixed with present (ie future) events. A very wellwritten and moving episode. For more info read the spoilers (but be prepared that doing so would ruin the emotional impact of the episode). I recommend watching the episode first.
So anyway, Fry discover his dog, Seymore, at the museum, and start a campaign to get it back. In the meantime we flash back to 1999 and see how Fry and Seymore meet, and how they become best of friends. Back in the future again Fry finally get his dog back from the museum. Farnsworth tell him that it's possible to clone a new dog using DNA from Seymore, preserved by the fossilisation process (think Jurassic Park here). Fry is estatic, he'll get his beloved dog back. So happy that don't even notice Leela and Amy wrestling, wearing very skimpy wrestling suits). In the mean time Bender feels pushed aside, and is sad that he might lose Fry. Back to 1999 we see Fry getting frozen, and how Seymore is the only one looking for him. He finally finds him at Applied Cryogenics, but his tireless efforts are to no avail. The cryogenics people ask Fry's parents to come get Seymore, and the do so, without discovering Fry. Back to the future; the crew is ready to start the cloning process in the basement (with a lavaspot nearby). Bender has had enough and throw the dog into the lava, in an attmept to get Fry back as a friend. Fry is devastated, and tell Bender that he would never dump him as his friend, he just wanted his beloved dog back. Bender is moved, and when Farnsowrth tell them that the rock around Seymore is of a particular hard variant (dolomite) that would allow Seymore to remain intact for a while, Bender dives in after him. He manages to get the dog-fossil back, and Farnsworth prepare to clone it. Just then Fry note that Seymore died at the age of 17 (?), and not apparently lived 12 years after he disappeared. Thinking that the dog lived a happy life, and probably forgot about him, he decides not to bring it back. At that moment it seems like the right decision. However the final scene is a flashback to 1999, showing Seymore waiting for Fry in front of Panuzzi's pizza. In a testement to the loyalty of dogs we see Seymore waiting patiently until the he dies, an old and tired dog, while a sad song play. The end.