OGR seems even more cryptic than proj:
ogr2ogr -t_srs "+proj=utm +zone=17 +datum=NAD83" -s_srs WGS84 outfile-utm.shp infile-geo.shp
Note the weird output-first convention. Check your UTM zone and datum. This approach seem to work for GPS tracks saved as GPX and converted using gpx2shp.