The extremely young cluster IC 348 has been monitored photometrically over five observing seasons from 1998 December 10 to 2003 March 26 in Cousins I with a 0.6m telescope at Van Vleck Observatory. Twenty-eight periodic variables and 16 irregular variables have been identified. The variability study is most sensitive for stars with I<14.3mag; at that brightness level, we find that 24 of the 27 known pre-main-sequence (PMS) cluster members in the monitored field are variables, illustrating the value of photometric monitoring for identifying PMS cluster members. Among this brighter sample, 14 of the 16 known K or M-type weak-line T Tauri stars (WTTS) were found to be periodic variables, while all five of the known classical T Tauri stars (CTTS) were found to be irregular variables. In the full sample, which includes 150 stars with I as faint as 18, we find that 40% of the 63 WTTS are detected as variables, nearly all of them periodic, while 55% of the 20 CTTS are also detected as variable, with none of them periodic.