The issue, which uses HTML to tell the device to run the reset code, applies to the stock Android browser but not to Chrome, so if you are on ICS upwards I would strongly recommend you avoid using the regular browser should your device be vulnerable.
The exploit has been confirmed working on a large number of Samsung devices (including some software releases on the Galaxy S III). You can test if you're vulnerable by crafting as a page shown below but, well, you're potentially gonna blow away your device in the process.
Additional USSD codes could potentially also be triggered doing further mischief on your device so it is quite a nasty issue and one that Samsung are apparently looking into now - we'll update the topic as further information becomes available.
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