Unpaired electron compound have a paramagnetic property that underlie dramatically relaxation enhancement and chemical shift perturbation (underlie by magnetic susceptibility shift)... As a consequences, all your signal can be vanished or be difficult to assign.

But, is not necessary the case. A more precise question can help to answer !

Typically in high-resolution solution-state NMR one would like to avoid any paramagnetic impurities to preserve narrow lines. As the previous poster wrote, the short relaxation times of the unpaired electron (ps to ns range in liquids) can result in line broadening or paramagnetic shifts (see for example Bertini, I., C. Luchinat, and G. Parigi, Solution NMR of paramagnetic molecules : applications to metallobiomolecules and models, in Current methods in inorganic chemistry. 2001, Elsevier, or of course Solomon's classic paper: Solomon, I., Relaxation Processes in a System of Two Spins. Physical Review Phys. Rev. PR, 1955. 99(2): p. 559.)

However, sometimes unpaired electrons can be helpful to obtain structural information in solution and solid-state NMR experiments (see: Nadaud, P.S., et al., Paramagnetic Ions Enable Tuning of Nuclear Relaxation Rates and Provide Long-Range Structural Restraints in Solid-State NMR of Proteins. J. Am. Chem. Soc., 2009. 131(23): p. 8108-8120).

Another application is Dynamic Nuclear Polarization. Here, the large thermal polarization of the electron reservoir is transfered to the nuclear spin bath by microwave irradiation. Signal enhancement factors of several orders of magnitude can be achieved, dramatically increasing the overall NMR sensitivity. The method currently experiences a renaissance due to the availability of high-frequency, high-power microwave sources (see: Maly, T., et al., Dynamic nuclear polarization at high magnetic fields. J. Chem. Phys., 2008. 128(5): p. 052211-19.)

In summary, as impurities unpaired electrons should most probably be avoided to obtain the best resolution. However, they can also be specifically used to obtain structural constraints or increase the overall NMR sensitivity.