We present Cu and Zn abundances for 38 FGK stars, mostly dwarfs, spanning a metallicity range between solar and [Fe/H] = -3. The abundances were obtained using Kurucz's local thermal equilibrium (LTE) model atmospheres and the near-UV lines of Cu I 3273.95 Å and Zn I 3302.58 Å observed at high spectral resolution. The trend of [Cu/Fe] versus [Fe/H] is almost solar for [Fe/H] > -1 and then decreases to a plateau <[Cu/Fe]> = -0.98 at [Fe/H] < -2.5, whereas the [Zn/Fe] trend is essentially solar for [Fe/H] > -2 and then slightly increases at lower metallicities to an average value of <[Zn/Fe]> = +0.18. We compare our results with previous work on these elements, and briefly discuss them in terms of nucleosynthesis processes. Predictions of halo chemical evolution fairly reproduce the trends, especially the [Cu/Fe] plateau at very low metallicities, but to a lesser extent the higher [Zn/Fe] ratios at low metallicities, indicating possibly missing yields.