The aim of our study was to analyse vegetables, potatoes and their products as sources of energy and nutrients in the average diet in Poland. Representative data of the 2016 Household Budget Survey from 36,886 households were used. This is the largest study sample in Poland, so we generalized the conclusions to the whole population using the statement ‘average diet’. We analysed three main product groups: vegetables, vegetable products, and potatoes and potatoes products, dividing them into 14 subgroups (e.g., tomatoes, cabbage, carrots, other vegetables, and mushrooms). The percentages of energy, protein, carbohydrates, total fat, nine vitamins (thiamine, riboflavin, niacin, vitamin B6, folate, vitamin C, vitamin A, vitamin D, and vitamin E), seven minerals (calcium, phosphorus, sodium, potassium, iron, magnesium and zinc), and fibre from the analysed food subgroups are presented. Additionally, the influence of household characteristics on the supply of energy and nutrients from each subgroup of vegetables, potatoes, and their products was evaluated using cluster analysis. In the analysis, R programme and Kohonen neural networks were applied. Our study showed that vegetables, potatoes, and their products provide 7.3% of daily dietary energy supply. Vegetables contribute more than 20% of the supply of six nutrients: vitamin C (51.8%), potassium (32.5%), folate (31.0%), vitamin A (30.6%), vitamin B6 (27.8%), and magnesium (20.2%), as well as fibre (31.8%). Cluster analysis distinguished three clusters that differed in nutritional supply from vegetables, potatoes, and their products. Educational level, income measured by quintile groups, village size, socio-economic characteristics, urbanization degree, and land use were the most important factors determining differences between clusters.