Section 7.3 of the paper describes several such examples.
On Sandy Bridge, for example, the result of the "AESDEC XMM1, XMM2" instruction is ready 8 cycles after XMM1 becomes available. If only XMM2 is on the critical path, however, the result is already available after a bit more than one cycle.
On Nehalem, the SHLD R1, R2, imm instruction has, according to Intel's manual, http://instlatx64.atw.hu/, and IACA, a latency of 4 cycles. Agner Fog reports a latency of 3 cycles. The measurements on uops.info show that the latency from R1 to R1 is 3 cycles, while the latency from R2 to R1 is 4 cycles.