The equation-of-motion coupled-cluster (EOM-CC) method has been used to calculate the vertical excitation energies of ethylene, trans-butadiene, cis-butadiene, and cyclopentadiene. The approximations used were the EOM-CC singles-and-doubles (EOM-CCSD) method and EOM-CCSD with a noniterative treatment of triple excitations, EOM-CCSD(T), EOM-CCSD((T) over tilde). The basis sets were atomic natural orbital sets augmented with diffuse functions. Comparisons have been made with a series of complete active space second-order perturbation theory (CASPT2) results, which used the same basis sets and geometries, and experiment. For the Rydberg states the EOM-CCSD results were in good agreement with experiment and CASPT2. The results for the valence states show more variation. For ethylene CASPT2 exaggerates the Rydberg character of the V state, while EOM-CCSD provides a better description. For the valence states of the other molecules the EOM-CCSD excitation energies tend to be too high, but considerable improvements are given by EOM-CCSD((T) over tilde). For the 1(1)B(u)/1(1)B(2) states of butadiene and cyclopentadiene EOM-CCSD((T) over tilde) agrees well with experiment and CASPT2. The agreement for the 1(1)A(1)-->2(1)A(1) and 1(1)A(1)/2(1)A(1) transitions for tuans-butadiene and cis-butadiene, which are not known experimentally, is not so good, with the EOM-CC results significantly higher than the CASPT2 ones. However, the EOM-CCSD((T) over tilde) and CASPT2 energies for the 1(1)A(1)-->2(1)A(1) transition in cyclopentadiene are in quite close agreement and both agree well with experiment. EOM-CCSD(T) shows an average error in vertical excitation energies for all states of all molecules of 0.12 eV, and improves those for valence states from an error of 0.26 eV for EOM-CCSD to 0.13 eV.