We fly non-precision ( VOR/DME and NDB ) approaches 9 out of 10 times using LNAV. It's even a recommended procedure in our company. Only when a circling is needed we put the MDA in the altitude window and use VNAV, otherwise its not allowed. For most airports the whole procedure including procedure turns and the missed approach is already in the databse, if not then we construct it ourselves. Of course we always monitor LNAV with raw data. On the 737-800 with it's GPS system, LNAV is always right on track.
We also do published GPS approaches using LNAV and VNAV. In this case the minimums are very close to CAT I ILS minima.
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