What is deemed to be a collectible autograph is different for each of us. You may want one from a person you have admired throughout history for their contributions. Others want something along the lines of politics, and they attend the various debates to collect these autographs from all the Presidential hopefuls. Celebrities including actors, musicians, and sports players are very common as well.
For many of us an autograph we get on our own by interacting with that celebrity is a collectible. We will treasure it forever and love to tell people all about it. We don't care if it has any monetary value associated with it either. We only want to remember the good time we had obtaining it.
For others, collectible autographs are those that they buy from dealers or other people. They generally don't end up meeting the person that signed it yet they really want to collect it anyway. The can cost about $10 or even $10,000 depending on who the celebrity is.
The fewer of them circulating the more collectible they are. For example Michael Jackson rarely signs autographs so anyone with one is sitting on a collectible that is worth plenty of cash. Those that are deceased including Marilyn Monroe and James Dean. Even though they have been dead for decades their legacy lives on.
Regardless of what your personal interests are, you will find plenty of collectible autographs out there that fit it. You can choose to buy one instead of clinging to the hope that you will one day run into your favorite icon and get one. Don't be afraid to ask for autographs though as most will be willing to do so as long as you are respectful of them.
If you don't get the collectible autograph on your own, be wary of where you do get it from. There are plenty of fakes out there circulating too and you don't want to get ripped off. There are some promoters out there that do have the direct access to various people though. They do have real autographs and they are cashing in on the desire other people have to own them.