Here are some homonuclear coupling patterns commonly observed in proton spectra (figs. 1-10). Heteronuclear coupling is described elsewhere.
The following nomenclature is used to describe coupling patterns. The letter A corresponds to the nucleus that is being split. The letters X, Y and Z are used to refer to nuclei coupled to A but with very different chemical shifts (or even different nuclei). The letters B and C refer to nuclei couple to A but with similar chemical shifts that lead to second order couplings. A prime mark (') is added to nuclei that are identical but not magnetically equivalent.
Fig. 1. AX coupling
Fig. 2. AX2 coupling
Fig. 3. AXY coupling: JAX ≠ JAY
Fig. 4. AX2Y coupling
Fig. 5. AXYZ coupling: JAX ≠ JAY + JAZ
Fig. 6. AXYZ coupling: JAX = JAY + JAZ
Fig. 7. AB second order coupling
Fig. 8. ABX second order coupling
Fig. 9. Two examples of AA'BB' second order coupling
Fig. 10. Two examples of AA'BB'C second order coupling