You need exactly:
If you are running your business on a $10/month shared host, expect to launch your business in one month, have no other expenses and have lots of potential customers who are willing to pay for your service already lined up you don't need a whole year's worth of money to start.
On the other side of the spectrum if you are planning a service that will need millions of dollars worth of servers, a team of developers and will start making profit in 3 years even 5 years of your salary won't get you very far.
I guess it depends on your business model, but three years seems excessive to me. When do you expect to start getting revenue? When do you expect to break even?
I think 1 year is a reasonable/realistic goal. You want to start getting revenue as soon as you can. Start selling your product as soon as you have a minimum viable product. Hopefully it doesn't take you three years to get to that point.
As other posters have said, three years seems like a lot; for anyone to save even a year's salary seems like pretty good going to me. qdot is right; it's more about your personal 'burn rate' than the money you brought in each year in the past - you may or may not be able to cut down on your running costs depending on your commitments (which of course is a lot to do with your family situation).
I think you should also be thinking about market opportunity - is space for the startup you have in mind going to get crowded the longer you leave it?
Another point: there is nothing saying you can't start your startup while you're still employed (which is for example what Balsamiq's Peldi did), but if you take this route, then it needs to be done with great care (e.g., looking after intellectual property issues, keeping your employer on-side, etc.). See, for example here.
My personal approach to limited savings has been to take a part-time consulting role and work on my startup the rest of the time (as per this question ). As the role is in a similar space as I my start-up, I get to learn about the needs of my perspective users on the job and thereby should deliver a better end product. Having said that, it's also pretty frustrating that progress is 50% of what I would achieve if I was working on the start-up full-time. This lack of progress is a bad thing for some startups, particularly when you need to get to market quickly (as per my earlier point). It turns out to be a good thing for me, as otherwise I would have delivered something truly useless by now!
You need enough to spend till you get cashflow positive on a monthly basis, and sustain it.
We did that in 10 months, but had a line of credit lined up in case we needed to go for anoher few months. In our software, if you don't make it 12-18 months then chances are may not make it at all.
3 years is no magic number and seems very high. But it does depend on the industry you are in.
Less money on hand forces you to be strategic on expenses, which is fundamentally good business practice. So don't look at less startup capital as a negative. Think about this : Can you atleast prove the business with this startup capital, if the answer is yes then go for it or else need more thought and planning.
It really depends on the type of the business, and potential exit strategies. If you expect revenues to counter the expenses in a year, getting revenue as soon as possible is a good idea.
You might be missing out on the explosive growth. Youtube had a tremendous rate of burning funds before it got acquired. It's all specific to your business, however, since I've seen startups launch with much less than a year of savings - one of which is quite successful but was started with about a month of savings.
Essentially, stop thinking about savings and years, start thinking about elasticity of expenses. You can probably live out of your office for 2-3 weeks, if you expect to find revenues in 2-3 weeks.. You can't, probably, stop paying for servers if you run Youtube, that would kill your company.