This is a question that every writer must ask himself at some point. The reason every writer must answer this question is because self-publishing is an available option for every writer. Things like age, sex, race, attractiveness, personal connections, and writing skill are irrelevant. Anyone can upload a file to Amazon, or Nook Press, or Kobo, or wherever. There are no barriers to entry.
Traditional publishing, of course, is a different animal. That option is not available to every writer for the simple reason that it takes two to perform this particular tango, and publishers refuse to dance with most writers. Only a small minority of writers are offered contracts.
So should you self-publish? I'm not going to try to answer that, because every writer must decide that for himself. Instead, I'll lay out the pros and cons of self-publishing, as I see them right now in March of 2015, and let you weigh them accordingly. (For simplicity, I'll use Amazon as a stand-in for all self-publishing platforms in general.)
No rejections. Getting rejected hurts, and self-publishing spares you this painful experience.
No waiting. Your book can be available to consumers the very same day you decide to self-publish it. With traditional publishing, your book becomes available according to their schedule.
More money. If your ebook is priced between $2.99 and $9.99, then Amazon will give you 70% of the list price for every sale. Even their 30% rate (for books priced outside that range) is better than what traditional publishers offer.
More frequent payments. Amazon pays every month. Traditional publishers do not.
Real-time sales data. You can watch the sales appear on your dashboard as they happen.
Cover art control. As long as it's not something that Amazon finds offensive, you can make your cover look however you want. You don't have to compromise with some in-house cover artist who thinks his "vision" of your story is better than your own. You can also change your cover whenever you want. I'm already on my second cover for Buddy, for example.
Content control. No compromising with editors who want to make major changes to your work that end up completely changing its plot or theme.
Pricing control. You set the price. If your sales slump, you can lower the price of your book at any time. If they rise, you can raise it. You don't have to worry about a publisher setting your ebook price at $14.99 or some other crazy figure.
Rights. You keep them all: digital, print, audio, film, foreign language, etc. You don't sign any rights over to Amazon when you self-publish. This also means you can un-publish your ebook whenever you want. This is important if you ever decide to gafiate.
You still have the option of being traditionally published at a later date. If your self-published book becomes a huge success, then publishing houses will come knocking.
And now the cons:
No validation. This isn't important to me, but it is very important to some writers. Those writers have a psychological need for someone in the industry to tell them that their book is worthy. Traditional publishing provides this. Self-publishing cannot.
You are responsible for your cover. You can make one yourself in Photoshop, or you can hire a cover artist to make one for you. If you don't have much art experience, making your own is difficult and risky. Hiring an artist is easier, but can get expensive. Expect to lay out at least $200 for a good cover. Average covers can be had for less.
Your book's blurb. You are responsible for it. Because a blurb is an advertisement, it's better to think of blurb-writing as a marketing skill instead of a writing skill. A great novelist can also be a terrible blurb writer, and vice versa, because prose and advertising copy are two different kinds of writing.
No help with marketing. If you want to market your book, you must do it yourself. The easiest way to do this is to buy ads. This can quickly get expensive, though. A better way to do it is to get involved in some social media outlet or other. This comes with its own dangers, though, because if people think you're just there to push your book, then they'll think of you as a spammer.
No in-house editing. If you want your book professionally edited, you have to pay for it yourself. This can get expensive. Expect to lay out at least a grand for a full-size novel. I edit my own work, but it's not easy, and I've had to learn a few tricks in order to be any good at it. Even so, I always want another pair of eyes to look it over, too.
No presence in bookstores. Even if you make a print version available, you will not see your book on a store shelf if you self-publish.
No legal team. If you run into any kind of legal problem, you must hire your own lawyer. You will not have the benefit of a traditional publishing house's legal team.
Professional associations. The one you want to join may not accept self-published authors as members. The SFWA, for example, has recently changed their stance on this matter, and they now allow indie authors, but if you're dead-set on joining some group, then you'd better read their membership requirements before deciding to self-publish.
That's all I can think of at the moment. I hope it gives you a better idea of what you're in for, whichever way you decide to go. Keep in mind that the industry is changing at light speed, and half of this information will be out of date in six months. Good luck!