Axl Rose is by far my favorite musician, and is known to be a good signer if you catch him at the right time.
With the exception in the video below, he seems to have moved away from signing a full "W. Axl Rose" when signing in recent years, and commonly will only sign with "Axl" in recent years.
I saw Axl at the Hard Rock Hotel in December of 2001. When he arrived, he was whisked directly inside by his bodyguard Earl (you can see him in "November Rain" and "Estranged" music videos), and I was even able to try to get his autograph. One of my collecting goals is a signed guitar.
There were limited sightings of him that weekend, but other members of the band were frequently seen in the main lobby and casino area chatting with fans, signing autographs, and taking pictures.
Hopefully with Guns N Roses touring again, collectors will see more authentic autographs and merchandise available!