A person who can openly joke about themselves is someone I want to be friends with. I have found that self-deprecating humor is also a great indicator of how stable and confident an individual truly is.
Humor reveals so much!
To the contrary of self-deprecation, have you ever met someone who is overly sarcastic and expresses their humor via mocking people? A more intense word for this type of behavior would be snide: "derogatory or mocking in an indirect way". Watch out for these people in your life, as they are often insecure. Some may not even realize it, but it makes them feel better to emphasize weakness in another. It is true that even with sarcastic people you should still be able to laugh at yourself, but it's important to know the difference between attacks disguised as humor, and when someone is just being good natured. The worst part of someone who mocks is that even if it's not funny, you must laugh since you are the subject matter. If you don't laugh, then you are at risk of being labeled too sensitive, even if the humor isn't funny. Oh, the dilemma!
Assuming you're not being overly critical or belittling yourself, self-deprecation shows you are willing to be vulnerable and transparent. You are confident enough in who you are as a person, that you find the weird or even weak things about you funny, not as something to hide or avoid. I find this trait incredibly attractive.
In conclusion, what does your humor say about you? Do you build up or tear down? Also, if you want people to relate to you and feel comfortable, show them you can laugh at yourself.