Alabama's history vs. Clemson is, admittedly, spare. I did find one historical clip of a game between the two teams from 1967, worth noting because coach Bryant provides the voiceover.
The two schools do share a number of connections, however, as most people already know. Clemson's legendary Frank Howard was a Tide alum, as is Danny Ford (whether his legend is smeared or not is up for debate). Tommy Bowden, of course, worked for a number of years in the state -- first at Alabama, then Auburn (and has been linked with the job in Tuscaloosa every time it's come open since 2000).
One more connection that you may or may not remember: back in 2001, the NCAA Committee on Infractions handed down those gruesome penalties which basically ruined Alabama's program for the remainder of the decade. The chairman at the time? You guessed it: Terry Don Phillips, Clemson AD.