Sufficient contrast is on of the 7 Things Every Designer Needs to Know about Accessibility.
The standard for web accessibility is the Web Content Accessibility Guidelines (WCAG) 2.0, which has several "success criteria" related to colour and contrast. The most basic success criterion related to colour contrast is SC 1.4.3, which says:
The visual presentation of text and images of text has a contrast ratio of at least 4.5:1, except for the following: (Level AA)
Large Text: Large-scale text and images of large-scale text have a contrast ratio of at least 3:1;
Incidental: Text or images of text that are part of an inactive user interface component, that are pure decoration, that are not visible to anyone, or that are part of a picture that contains significant other visual content, have no contrast requirement.
Logotypes: Text that is part of a logo or brand name has no minimum contrast requirement.
The primary target group of this success criterion (SC) is people with colour vision deficiencies, but fulfilling this criterion also makes sure that contrast isn't too low for the population at large (or at least most of them; see also SC 1.4.6, which requires a contrast ratio of 7:1).
Insufficient contrast is a very frequent issue, as Julie Grundy points out in her article Three common accessibility pitfalls for developers: colour contrast.
There are many tools to help you either check contrast or find accessible colour combinations, for example: