I don't think these have been mentioned:

For Nabisco Premium Saltine Crackers (circa 1964):

Premium Saltine reclosable pack,
You open 'em up and you close 'em back.
They stay crisp until
You get to the very last cracker.
Premium Saltine!

Fig Newton (same era):

The one and the only Fig Newton is a very remarkable thing...
(don't remember the rest, although the tune's still with me; may have been a girl on a tree swing in the TV commercial; anyone?)

It ended with: The one and the only Fig Newton is a very remarkable, very remarkable, very reMARKable thing!"

Others have mentioned a couple of sixties-era Chef Boyardee commercials (e.g. the "French school kids" one for Spaghetti and Meatballs: "Come when the bell calls (tolls?), spaghetti and meatballs"; and, another for Ravioli: "Ravioli, we like ravioli..."). There was a third one in that series, I believe for Beefaroni, featuring "British" school children. I don't know the name of the "English sounding" tune was or all the words, but there was something about "oodles and oodles of big (tasty?) noodles, and beef, tomato and cheese" -- or something like that.

But the one I wish had *never* aired was for Del Monte canned juices. I was in fourth grade when this one was popular and my last name was "Belmonte" back then, so you can imagine the rest:

Del Monte fruit juice drinks, so fresh, so light.
Del Monte fruit juice drinks -- good morning, noon or night!

Fill in the gaps where you can. Hope I helped folks remember some more jingles/ads.