We present VLT FORS1 and FORS2 spectra of 39 candidate high-redshift supernovae that were discovered as part of a cosmological study using type Ia supernovae (SNe Ia) over a wide range of redshifts. From the spectra alone, 20 candidates are spectrally classified as SNe Ia with redshifts ranging from $z=0.212$ to $z=1.181$. Of the remaining 19 candidates, 1 might be a type II supernova and 11 exhibit broad supernova-like spectral features and/or have supernova-like light curves. The candidates were discovered in 8 separate ground-based searches. In those searches in which SNe Ia at $z \sim 0.5$ were targeted, over 80% of the observed candidates were spectrally classified as SNe Ia. In those searches in which SNe Ia with $z > 1$ were targeted...