There is at least three places you need to set the maximum upload file size in WordPress.
First check your php.ini
upload_max_filesize = 64M;
post_max_size = 64M;
Restart Apache after making this change.
Then if you are using WordPress multi-site, you need change a setting in the backend. Visit My Sites -> Network Admin -> Dashboard -> Settings -> Network Settings. Then scroll down to the Upload Settings area and change that.
Thanks to dorr13 for that tip.