Two-dimensional COSY (COrrelation SpectroscopY) experiments allow you to determine the connectivity of a molecule by determining which protons are spin-spin coupled. Of course, one could accomplish the same task by a detailed analysis of spin-spin splittings, given high enough resolution. Nonetheless, COSY spectroscopy, when practiced with the aid of magnetic field gradients, is a quick method of establishing connectivity.
In the example shown below the proton spectrum for ethyl benzene is plotted on each of the two axes. Note that the diagonal within the box is also the spectrum for ethyl benzene as seen from "above." Off-diagonal peaks denote splitting between protons on adjacent carbons. Note the coupling of the methyl protons at 1.1 ppm to the methylene protons at 2.8 ppm. The aromatic multiplet at 7.2 ppm is coupled with itself. Also note that neither the methyl or methylene protons are coupled to the aromatic protons at 7.2 ppm.
This COSY experiment gives information regarding three-bond couplings (from a proton to its carbon, to the adjacent carbon, then to that carbon's proton). More extensive COSY spectra may be generated by advanced techniques, allowing one to view four-, five-, and occasionally six-bond couplings.
Finally, another class of experiments, know collectively as nuclear Overhauser effect (NOE) experiments, provide information on through-space rather than through-bond couplings. Such experiments are very important in the use of NMR to establish tertiary and quarternary structure.
Spectrum of Ethyl Benzene:
(Click on the spectrum to obtain a magnified view.)