Heinz Baked Beans by the Who
The BBC didn’t allow names of products on the air. “Kodachrome” wasn’t released as a single in the UK for that reason. However, the Kinks wanted the airplay, so they redubbed the line.
Alvin Crow and the Pleasant Valley Boys: Nyquil Blues.
*Gimme a bottle of Nyquil
That restful sleep my body needs
Analgesic decongestant with a antihistamine
*
I just can’t be satisfied unless my tongue is green.
Yea. Hey Little Cobra counts. I’m not sure if 409 does. It’s not a brand though it refers to a specific manufacturer’s engine.
Like cars, songs with the brand names of alcoholic beverages could be a sub-category.
“Rednecks, White Socks, and Blue Ribbon Beer” - Johnny Russell.
Pass the Courvoisier
Gucci Gucci
Air Force Ones
My Adidas (even non-hip-hop heads anywhere close to my age should know that one)
Cover of the Rolling Stone by Doctor Hook and the Medicine Show
Janis Joplin - Mercedes-Benz
Dinah Shore: “See the USA in your Chevrolet.” 
Pop Rocks and Coke - Green Day
I Only Drink Bud - The Queers
2000 Flushes - Chixdiggit!
And if we count puns on the brand name:
Harley David (Son of a Bitch) - Serge Gainsbourg (covered in English by the Bollock Brothers)
(Warning: link contains general Fugishness.)
Another catagory that probably has a lot of entries: Sports teams fight songs.
Go Cubs Go and Bear Down, Chicago Bears are the two most familiar to me. There’s also Let’s Go, Go Go White Sox for the southsiders. The Super Bowl Shuffle probably counts, too.
Call Ticketron - Run the Jewels
Superbird - Fu Manchu
Slick Black Cadillac - Quiet Riot
The Jeeps, the Lex Coups, The Bimaz and the Benz - Lost Boyz
“It Was A Very Goodyear”
(Okay, start nitpicking)
“Novacane” and “Nikes” by Frank Ocean
“Novacane” (different song) and “Fuckin With My Head (Mountain Dew Rock)” by Beck
“Novocaine For the Soul” by Eels
“Date with Ikea” by Pavement
“From a Motel 6” by Yo La Tengo
Songs without links above are NSFW; they’re linked below.
“Novacane”
“Nikes”
“Fuckin With My Head (Mountain Dew Rock)”
“Little Red Rodeo,” by Phil Vassar.
About an Isuzu Rodeo SUV, of course.
Grapefruit - Juicy Fruit. Jimmy Buffett.
Also Meet the Mets and Here Come the Yankees
And for show titles Joseph and the Amazing Technicolor Dreamcoat
Superball - Helium
Barbie Girl - Aqua
Twist Barbie - Shonen Knife
Tortoise Brand Pot Scrubbing Cleaner - Shonen Knife