At present Opera (version 10.5 onward), Safari (version 5 onward) and Chrome (version 5 onward) all support the individual border-*-radius properties and the border-radius shorthand property as natively defined in the current W3C Specification (although there are still outstanding bugs on issues such as border style transitions, using percentages for lengths, etc.).

Mozilla Firefox (version 1.0 onward) supports border-radius with the -moz- prefix, although there are some discrepancies between the Mozilla implementation and the current W3C specification.

Safari and Chrome (and other webkit based browsers) have supported border-radius with the -webkit- prefix since version 3 (no longer needed from version 5 onward), although again with some discrepancies from the current specification (see this article for further details of how older versions of Webkit handle border-radius).

Even Microsoft have promised, and demonstrated in their recent preview release, support for border-radius from Internet Explorer 9 onward (without prefix).