Do you ask your guests to sign the wedding guest book after the wedding?

I wouldn't track people down after the wedding to ask them to sign it. Plenty of people just prefer not to sign guestbooks or they simply don't think it's an important detail. In the greater scheme of things, it's not that important, so I wouldn't make a thing of it after the fact.

On a side note, I will sign a book if I happen to see it when I have a minute, but I rarely do any of the other other things (like providing advice on a card or signing something decorative like a quilt square of picture frame matting). I HATE my handwriting so no one wants it on permanent display. And I doubt my husband has ever signed a guestbook in his life.

There's no such thing as getting every single guest to sign it at any wedding.

I wouldn't track people down to get them to sign it. If they really want to they would have or they will bring it up to you when they see you. Just like with high school year books you aren't going to have every single person sign it.

You could write their names in yourself if you are just looking to commemorate all who were there

I agree that it's probably not worth tracking people down, but if they are bridal party members who were just too busy and you see them pretty often, I definitely think it would be worth asking next time you see them! Maybe just leave it in an obvious place in your house for a while and when people come over who were at the wedding, ask if they would like to sign it.