Cytosine can undergo modifications, forming 5-methylcytosine (5-mC) and its oxidized products 5-hydroxymethylcytosine (5-hmC), 5-formylcytosine (5-fC) and 5-carboxylcytosine (5-caC). Despite their importance as epigenetic markers and as central players in cellular processes, it is not well understood how these modifications influence physical properties of DNA and chromatin. Here we report a comprehensive survey of the effect of cytosine modifications on DNA flexibility. We find that even a single copy of 5-fC increases DNA flexibility markedly. 5-mC reduces and 5-hmC enhances flexibility, and 5-caC does not have a measurable effect. Molecular dynamics simulations show that these modifications promote or dampen structural fluctuations, likely through competing effects of base polarity and steric hindrance, without changing the average structure. The increase in DNA flexibility increases the mechanical stability of the nucleosome and vice versa, suggesting a gene regulation mechanism where cytosine modifications change the accessibility of nucleosomal DNA through their effects on DNA flexibility.