Most anything off Hawkwind’s Space Ritual album. It was recorded back when Lemmy was still in the band.
Perfect Kiss by New Order
Black Flag’s “Six Pack” starts off with a long stretch of nice, driving bass accompanied by nothing but some skeletal drums. And it’s a song about DRINKING!
Beat me to it. Actually, the Police had a lot of songs with good bass lines, including “Spirits in the Material World,” “Every Breath You Take,” and “Synchronicity II.”
Blood and Roses by The Smithereens. Not flashy, but catchy as all hell.
Also, several Jane’s Addiction songs - particularly Ted, Just Admit It… and Three Days.
Which is a direct ripoff of Queen & David Bowie’s “Under Pressure.”
How’s about “Boris the Spider” by The Who?
No no no no no, cuz, y’see, it’s, like “duh duh duh duh duh DUH duh”. Y’see? It’s, like, totally different.
Anything by 311, especially “What was I thinking?” for a good bass-driven track and “Feels So Good” for a good solo.
Anything by Rancid or Operation Ivy (same bass player), especially “Hoboken” and track 16 on Rancid’s self-titled album (don’t know the name.)
Anything by Primus. “Here Come the Bastards” comes to mind, but that whole album is great (Sailing the Seas of Cheese.) As has been mentioned in this thread, Les Claypool is a bass god.
“5446 (That Was My Number)” by Toots and the Maytals has a very good, very simple, very catchy bassline.
Every song by Dream Theater has kickass bass. Of course, the other four instruments are even more kickass, so it’s hard to notice. 
But sometimes I’ll tune out every other instrument in “Under A Glass Moon” or “Only A Matter Of Time” and just hum along with John Myung’s bass line.
Iron Maiden has some of the most unique bass work in heavy metal. Real chugga-chugga. Steve Harris plays bass like a rhythm guitar.
Of course, for sheer no-frills in-your-face brutality, nothing beats Motorhead.
The Pixies have a ton of good songs with good basslines, as do Echo and the Bunnymen.
“Mystery Achievement” by the Pretenders.
Somewhat obscure, but I will emphatically recommend Snowbound, from Donald Fagen’s solo album Kamakiriad. It’s a Steely Dan tune in all but name, and Walter Becker’s bass track is the centerpiece.
A simple but really catchy bassline is in Bowie’s “John, I’m Only Dancing”. An utterly fiddly but very cool bassline is the intro to the Faces’ “Three-Button Hand Me Down”. - the ability to play this at audition won Glenn Matlock his place in the Sex Pistols. And of course Herbie Flower’s bass in Lou Reed’s “Walk On The Wild Side” pretty much makes the song.
“What They Say” from Redd Kross has one of the best.
“Badge” by Cream
“Slip it in” By Black Flag leads in with the bass, then everyone joins in.
“So What” by Ministry
Some of the coolest bass parts can be found on the first three songs on Can’t Stand The Rezillos by The Rezillos, of course. *Flying Saucer Attack, No, * and Sombody’s Gonna Get Their Head Kicked In Tonight.
Another cool line is in Taxman by The Beatles, also appropriated for Start by The Jam.
Chic - just about anything - but Le Freak and Good Times are special - John Deacon admits to ripping off ‘good times’ for Another One Bites The Dust;
I like Bruce Thomas’ playing with the Attractions; I Dont Want to go to Chelsea, Party Girl, 13 Steps Lead Down, many others.
Can’t recall his name (Leon something?) but George Michael’s bass player is the dog’s bollocks. Listen to the song ‘Faith’ purely for the bass; awesome.
I was listening to Joni M’s Shadows and Light yesterday - Jaco Pastorius could play a bit too.
MiM
However, re-reading your OP you could be looking for catchy lines rather than great playing so;
Peaches by the Stranglers
Dancing in the Moonlight by Thin Lizzy
Superstition by Stevie Wonder
Good Times by Chic (again)
Tempted by Squeeze
Pump it Up by Elvis Costello
Sustitute by The Who
MiM
Whole World is Africa - Black Uhuru
Excellent choice.
I always found the bass line from “Superfreak” by Rick James (biotch!) to be pretty catchy, in the simple-but-fun catagory.
Joy Division and the original goth bands often treated the bass as a rhythm guitar. Both albums proper (*Unknown Pleasures * and Closer) have excellent basslines.