Self-parody is an important method for breaking loose from stereotypes and entrenched views in a light-hearted way. Being able to poke fun at oneself allows for critical scrutiny of perceived fundamentals, which may reveal unpleasant truths as well as promote personal growth. At the same time, nothing is funnier than an accurate jab at a hallowed truth held evident by the person delivering it.
There are those with the gift for parody and self-deprecation and those without. Funny people, willing to take themselves down and have fun at their own expense, should indeed carry on. Those who do it solely for the purpose of appearing to have humor on themselves typically just come across as stiff.
Self-parody is a form poking fun at yourself. It can be funny if you are clever in how you orchestrate the parody. However, it could also be very annoying and not funny at all. If you can not laugh at yourself, who can you laugh at? It is always good to not take things too seriously, but there is a limit to when it can be funny and then just be irritating.
Sometimes self-parody can be hilarious, especially when it's done with wry humor and a good sense of self-awareness. Some celeb self-parody movie cameos, like Kareem Abdul Jabar in Airplane and most especially Wayne Brady in the Chappelle Show are freaking hysterically funny. Even celeb stints on the Simpsons - like Lady Gaga and the Rolling Stone self-parodies are very funny.