Here I will attempt to break down every model of barked Rolex ever made. If I've forgotten one, please let me know. Pics from various internet sources.
NON-QUICKSET (debuted in mid-1960's)
1807
1807 with reverse-barked bracelet (outer links barked instead of inner link)
1807 in white gold
SINGLE-QUICKSET (debuted in late 1970's)
18048 (engine turned + barked bezel. Shown with onyx dial)
18078 (standard barked bezel. Shown with sandstone dial)
18079 (standard barked bezel. White gold model)
18108 (Barked bezel with 12 diamonds. Here's
one with a rare dial)
18308 (Barked bezel with 12 diamonds. I'm unsure of the difference between 18308 and 18108)
18348 (Full diamond bezel)
DOUBLE-QUICKSET (debuted in late 1980's)
18248 (engine turned + barked bezel. Shown with wood dial)
18249 (engine turned + barked bezel. White gold model)
DATEJUSTS (Check out those barked jubilee bracelets!)
1607
1607 in rose gold (The only barked rose gold Rolex)
16078 (Shown with houndstooth dial)
16248
6927 (26mm ladies' model)
69278 (26mm ladies' model, shown with tiger-eye dial)
Ladies' Pearlmasters also exist in barked versions. Anybody know the model number of that one?
MISC.
5100 (This rare early Rolex quartz model was available barked)
1511 (The only 34mm barked Rolex)
1807 with Morellis Finish (This isn't actually barked, but sometimes people mistakenly call it that)
Prototype white gold Submariner Date (Bracelet is barked. The watch shown went for $600k+ at auction. There are only 3 prototypes like this
according to Hodinkee)