This study aimed to evaluate the heritability (h²) estimates of some important udder conformation traits, their relationship to each other and with production, and their phenotypic and genetic trends over a 10-year period in relatively high-yielding Holstein-Friesian cows. A total of 15,032 cows from six herds in Hungary were tested for milk (MY), butterfat (FY), and protein (PY) production yields over 305 days in first lactation. In addition, their udder conformation was scored for udder attachment (FU), rear udder height (RUH), central ligament (CL), udder depth (UD), front teat placement (FTP), and udder texture (UT) on a 1–9 linear udder score scale. REML and BLUP single-step animal model and linear regression model were used for data analysis and estimation. The production traits of the cows were quite reasonable, with 10,179.4 kg milk, 380.3 kg fat, and 333.1 kg protein in a standard lactation of 305 days. The scores of the udder conformation traits (5.4 to 6.1) were slightly above the mean of 5 on a linear scale of 1–9. The h² for MY, FY, and PY were obtained from 0.30 to 0.35, while those for udder traits were from 0.22 to 0.41. Phenotypic (rp) and genetic (rg) correlations for the relationship between production and udder conformation were weak or negligible (ranged from −0.33 to +0.15). Most of the associations between different udder traits were generally weak, but moderate positive correlations were observed between FU and UD (rp = 0.42, rg = 0.50 or 0.57), and between FU and UT (rp = 0.36, rg = 0.33 or 0.35). There were increasing genetic trends in the milk production (b = 2.2 to 16.5), but the studied udder conformation traits did not change over time (b = 0.00 to 0.03). In our study, despite an increase in milk yield over the studied ten-year period, udder conformation traits did not change. Therefore, considering that udder conformation scores were slightly above average and that udder traits were included in the selection index, we believe that it may be necessary to reconsider the udder conformation scoring system and its inclusion in the selection index.