I am local and AP holder, so other than my visits in 1996, before I lived here, my visits aren't actually travel. Most of my visits are solo, and it's fabulous!
There are many aspects to take advantage of. Single rider lines!!

Getting to ride something like Expedition Everest over and over and over - even if the park is packed! Dining options often expand - it's not uncommon to be able to get into a popular dining venue just by showing up, since it's more likely they might still have that small table available that the families can't use. I've had that happen at Cinderella's Castle before.
No compromise! You can visit what and when you like. You also travel from place to place much more quickly without the entourage.
I really enjoy interacting with people in queues, or even just relaxing and having a cold beverage. It's so easy to strike up short conversations with fascinating people from all over the world - you're all sharing a special experience in a magical place, and that breaks down all sorts of barriers. Most cast members are incredibly kind and easy to interact with, and as another poster stated, it's actually easier to converse with them when you are on your own. It's hard to explain, but they seem to actually give a little more attention to you when on your own.
Same with the characters, they seem to give their own type of special attention to a solo adult. I also get a kick out of interacting with face characters (who can talk to you). They never, never break character and are fabulous at presenting the magic, yet still interacting with you as an adult and not a child.
Oh, and hugs. Sometimes I've lined up for character meet & greets just to get a hug. Hint - Goofy usually gives the best hugs
