Have you noticed that Abe Simpson seems to appear in random places and only be recognized as "old man"?
This is because Abe Simpson is the ideal American Senior Citzen. He represents the whole of the aging community. Abe is reckless, yet full of compassion for those close to him. When he babysits, he gets the job done (even if he sleeps the whole time). When wants something, he gets it. Take for example the father-son partnership between Abe and Homer when they created a "love potion". He smelled success and grabbed it by its tail (Does success have a tail?).
Abe is also a crime fighter. As Maggie's counterpart, (see article on Maggie) he even helped in the apprehension of Springfield's worst criminal, The Cat Burglar. Even if the cat burglar was his next door neighbor and he didn't figure out it was him for a LONG time, he still got the job done.
Abe also has a sensitive side, as seen in the episode where he falls in love with a neighbor in his old age home, Bea. Bea dies and leaves a small fortune to Abe. Abe has a dilemma of what to do with the money, and in the end, he decides to donate it to his old age home so that they can remodel it and construct a new dining hall.
Abe is a great rolemodel, father, grandpa, and husband, who looks alot like Homer. So the next time you see Abe on TV, think to yourself "What would this show be without Abe?"