The first priority for me is to get some money set aside for emergencies. An emergency fund of even $1,000 can pay for many unexpected things that life can throw at you. This is your own personal insurance policy and should be set aside with a sign "Emergency Exit Only." If you have no savings, this is the first priority with the plan that this emergency fund will grow into savings in the amount of 3-6 months worth of expenses (your personal reserve).
The next priority is to pay off all debt, except the mortgage on a house. This goal should come after saving for your initial emergency fund but before you build your personal reserve of 3-6 months worth of expenses. There are two main methods of paying off debt: 1) paying off the debt with the highest interest rate first and 2) paying off the debt with the lowest balance first. The numbers show that the first method is the most beneficial financially because less interest is paid overall. On the other hand, the second method has proven to bring debtors greater satisfaction as individual debts may be knocked out sooner. Read more under "Avoid Debt."
Next on the priority list is saving for retirement. A good rule of thumb is 15% of your gross income. If you can afford 20%, then do that to take advantage of available tax deferrals or tax-free growth. You can usually get 6% or so into a 401(k) from an employer. The rest can usually go into a Roth IRA. The maximum contribution for a Roth IRA is now $5,500 beginning in 2013. Depending on your income, that may or may not reach your 15%. If it doesn't, you can increase your 401(k) contributions to make up any difference.
Once you are fully funding retirement, the next priority is education savings for the children. There are tax-advantaged education account types, similar to the Roth IRA, called Coverdell or Education Savings Accounts and 529 Savings Plans. These also help avoid taxes as long as the money is used to pay for education. When it comes to funding education, a last resort can always be taking out a student loan if you don't have enough saved and don't qualify for scholarships or student aid, but you can't take out loans for retirement. This is why retirement is always a higher priority than education. Read more under "Where Should I Save Money for My Kids' Education?" and "Why I like Coverdell Education Savings Accounts."
After all of this, you may consider paying off the mortgage on the house early. One reason that paying off the mortgage early is lower on the priority list is because of such low interest rates these days. With good credit most home-buyers can lock in a mortgage rate below 3% or 4%. The logic behind not paying off the mortgage early is this: when you pay off your mortgage you are in essence getting a return on your money of about 3-4%, or whatever your mortgage interest rate is. If you were to invest that same money in a mutual fund, you would most likely get a return in the range of 5-10%, depending on the investment. This is obviously a better return on your investment than paying off the mortgage. If interest rates were higher, then this might not be the case and it could be better to pay off the mortgage than invest in a mutual fund, but that is a case to be analyzed at a future day when interest rates are higher.
In the end, there should be a method to the madness of trying to save money. These priorities will aid you in reaching certain financial goals and give a foundation on which to lay your financial decisions as you are faced with how to allocate your money.