What percent of salary should go towards retirement vs. emergency savings? Should some be set aside each and every pay for emergencies?
Though I do think it is important to have a diversified portfolio for your retirement, I also think it's more important to make sure you are at no point touching this money until you retire. Taking money out of your retirement early is a sure fire way to get in a bad habit of spending this money when you need a little help. Here's a tip: If you consider this money gone, you will find another way to figure out your situation.
With that said, I also would rather not put a percentage on this. Start by building your emergency fund. You'll want to treat this like a bill and make a monthly payment to your savings account each month or paycheck. When you have a good nine times your monthly income in here, stop contributing to this fund. Instead start putting the same amount into your IRA instead. At this point you should no longer have to add to your emergency fund unless there is a true emergency and you are replacing that money. Keep in mind that the amount of money in your emergency fund changes significantly in each situation. Sit down with your bills and think about how much money you would need in the event you lost your job. How long would you be out of work? How many bills do you have each month that would need to be covered?
I think rather than take a percentage out, I focus on getting a total amount I consider appropriate for my emergency fund. Then as for retirement, I do at least what my employer matches, up to the contribution limit. For example my personal retirement plan in the US has an annual max contribution of $5000.
Once I have my 6 to 12 month emergency fund (in a pretty liquid form) and a fully funded retirement, I want to concentrate on building wealth via investments or increasing the quality of my life by spending.
Summary answer is: no percentage for emergency, just get to a total amount you feel comfortable. Then whatever percentage will allow you to make the most of employer matching and make your retirement fully funded.
A well diversified retirement portfolio is going to have some component in cash or near-liquid investments. So I tend to put it all in one place knowing that I can draw on it (at least from the ROTH account) in the event of an emergency.
Obviously, you don't want to do this very often, but hopefully emergencies don't happen often either. You also have to attenuate your idea of an emergency so that it doesn't mean "I didn't get a bonus check this year and can't afford gifts for the kids as nice as last year!"