But if you really want to be sure, you can grab an app from Zimperium Labs, the organization responsible for uncovering Stagefright.
When you download and launch the app, it pulls up a list of the specific CVEs (common vulnerabilities and exposures) that impact your phone.
Of course, if you’re susceptible (and unless you’ve applied the patch, you are) Zimperium throws in a “Contact Us” button to give out your email address, phone number, and other details that would presumably give Zimperium a method to reach out to you. For what reason, they don't say.
This and other issues were noted in the comments, with some complaining that they had just installed Sprint’s patch for their Samsung device, yet they were still told they had the vulnerability. So perhaps the patch didn’t work, or Zimperium may just be checking the device information against its database, which hasn’t yet accounted for the new patches.
The story behind the story: Stagefright is likely the most significant vulnerability to hit Android. However, it’s spurred Google, Samsung, and LG to take unprecedented steps to issue regular security updates. If the major Android players can follow through, and if carriers don't get in the way, it could mean a much safer ecosystem for everyone.