There are two ways:
1) Elevate your application so that it has the required permissions
2) Stop using the Registry.
Access to the Registry is becoming more and more restricted and is likely to be become even further restricted rather than less - mostly because it was badly overused in the past. Unless you absolutely need to examine existing values, then I would strongly recommend that you do not use the registry for anything. There are better places and ways to store your data which will be available in future OSes.
However, if you have to do it, you can elevate your app :
http://support.microsoft.com/kb/981778[
^] - however this will engage the UAC and require explicit confirmation from the user.
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