cURL doesn't provide a CA bundle any more [1], it's the job of your OS to provide this. As I understand it, all tools that provide SSL support will fail safe if there are no root CAs on your system.
[1] http://curl.haxx.se/docs/sslcerts.html
$ pacman -Qi ca-certificates | grep 'Required By'
Required By : ca-certificates-java curl glib-networking neon qca qt4
Note that curl is on that list but wget isn't.But the point halfasleep is making is important: Don't assume either wget or curl will validate your SSL connection because it may not have been set up by your OS/distribution.
[1]: http://curl.haxx.se/docs/caextract.html