libeay32.dll and ssleay32.dll have to be path-accessible for php_curl.dll loading to succeed.
But copying them into Apache's ServerRoot, Apache's \bin\, Window's \System32\, or even worse into the Windows main directory is a bad hack and may not even work with newer PHP versions.
The right way to do it is to add the PHP path to the Windows Path variable. In Control Panel -> System click on Advanced System Settings and use the button Environment Variables. Under System Variables you will find the Path variable. Edit it and append ;C:\PHP prepend C:\PHP; to it - or whatever the path to your PHP folder is. Then fully stop Apache and start it again (a simple restart might not be enough).
Update 2017-05:
I changed the instructions above to prepend the Path variable with the PHP path instead of appending to it. This makes sure that the DLLs in the PHP path are used and not any other (outdated) versions in other paths of the system.
Update 2018-04:
If you have already chosen the wrong way and copied any of the PHP DLLs to Apache or Windows paths, then I strongly recommend that you remove them again! If you don't, you might get into trouble when you later try to update PHP. If a new PHP version brings new versions of these DLLs, but your old DLLs still linger around in system or webserver paths, these old DLLs might be found first. This will most certainly prevent the PHP interpreter from starting. Such errors can be very hard to understand and resolve. So better clean up now and remove any of the mentioned DLLs from Windows and Apache paths, if you copied them there.
(Thanks to @EdmundTam and @WasimA. for pointing out this problem in the comments!)
