I got this Base64 gif image:
R0lGODlhDAAMALMBAP8AAP///wAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA
AAAAACH5BAUKAAEALAAAAAAMAAwAQAQZMMhJK7iY4p3nlZ8XgmN
Very old question, but as of iOS7 there is a new, much easier way to do so, hence I'm writing it here so future readers can use this.
NSData* data = [[NSData alloc] initWithBase64EncodedString:base64String options:0];
UIImage* image = [UIImage imageWithData:data];
Very easy to use, and will not hit the 2048 byte size limit of a URL.