I quit my day job back in 2008 and it's probably the best thing I've ever done. The first year or so sucked in terms of work hours and financial security. I had to drop all my day job income to scale up the non-job income and my income and credit both took a hit in the short-run. Today, however, life is amazing.
1. Security - Over the years, I've built up a nicely diversified stream of income. Sure, some of them slow down or disappear from time to time, but the odds of me losing even 50% of my income overnight are so low that if it happened, it would likely correspond with some kind of catastrophic societal collapse. On the other hand, I've watched several good friends (and my dad) lose their jobs with no notice this year - and often, no severance. If you're like most single people, losing your job = losing 90% or more of your income.
2. Task flexibility - If I start to hate a part of what I'm doing, or if there's a segment of that income stream I don't like doing, I don't necessarily have to keep doing it. I might decide it's unpleasant but worthwhile, or I might decide to move in another direction or outsource the task. There's no boss to say I have to stick with it or personally complete it.
3. The "work in your pajamas" factor - I usually don't, but it's not uncommon for me to work in a golf outfit, yoga pants, or a bikini/swimsuit coverup depending on what I intend to do that day. Depending on the dress code of your day job, you might also save a lot on work clothing.
4. No artificial caps on income - Instead of relying on a boss or HR department to give you raises (often limited by what everyone else there is getting, or some annual percentage cap), I can work harder/smarter and increase it indefinitely. This has worked out very well.
5. No coworkers - Some people would call this a drawback, but I love it. I'm an introvert, and I get more than enough social interaction by joining clubs or taking classes (and I've met a very diverse and interesting group of people in doing so).
6. You can do things when it's most efficient - I do my shopping on weekdays, I drive mostly outside of rush hour, and I tend to vacation mostly in the off-season and shoulder seasons. In doing so, I save an incredible amount of time and money.
7. Greater control over your priorities - Let's say something happens and if you don't take action RIGHT NOW, your company will probably lose money, a client, an opportunity, whatever. If you have a boss, that boss is going to want you to deal with it immediately. If you work for yourself, you can decide whether it's really that important, or if you'd rather enjoy your evening/vacation/etc. and let things fall where they may (and most things aren't as urgent as they seem, so it often works out anyway).
8. Flexibility in terms of hours worked - Yes, some jobs really do offer this, but they're few and far between - and in many cases, a job billed as "flexible" just means the boss wants to be able to use you at any hour of the day. Similarly, most jobs do want you accountable and at a desk SOMEWHERE for at least 40 hours/week and some portion of the business day. Working for myself, I can get my work done in a few hours and then go do something else. Yes, there was a time in the beginning when I worked insane hours, and yes, I've had occasional bouts where procrastination allowed 3 hours of work to swallow an entire day - but on the whole I work much, much less than almost everyone I know (while earning more). Sometimes I feel guilty about it.
9. So much free time - Working 40-60 hours/week, commuting, and getting ready for work takes up a lot of time (slightly more if you're female and you have to dress up). I sometimes go back home to the Midwest for weeks or months at a time and my grandma and I do tons of stuff together because my free time approaches that of a retired person. It's not automatic with self-employment, but it's certainly more possible than if you have a day job.
I'm sure there are other pros I'm not thinking of at the moment, but I get bad feelings just thinking of what it was like to have a day job. It's not for everyone, but for me it's a night and day difference in terms of quality of life.