Carbon satellites can be used to obtain structural information, which is not available by looking at the main peaks in the NMR spectrum.
This usually occurs when the purely C compound is symmetrical but where the 1% of the compound which has a C atom in it is no longer symmetrical.
For example, it is not possible to tell whether stilbene (Ph-CH=CH-Ph) has a cis- or trans- double bond just by examining at the main peaks in the H NMR spectrum. The =CH- proton does not couple to the adjacent =CH- proton as the molecule is symmetrical. However, 1% of the stilbene molecules will have a C atom on one of these double bond carbons (i.e. Ph-CH=CH-Ph). In this situation, the proton adjacent to C atom will couple to the C atom to give a wide doublet. Also, as this molecule is no longer symmetric the C= proton will now couple to the adjacent C=  proton, causing a further doubleting. Thus, this additional coupling (additional to the C coupling) is diagnostic of the type of double bond, and will allow one to determine if the stilbene molecule has a cis- or trans- configuration i.e. by examining the size of the diagnostic J coupling constant from -CH=CH- bond. Thus, only a single 1H NMR spectrum is needed, albeit with close inspection of the satellite peaks, rather than any further complex NMR or derivative chemical experiments.
The same would be seen for 1,2-Dichloroethene.