Eliminating debt and steadily investing is the safest way to great wealth, though it is hardly the most exciting. Creating a loose, lifelong financial plan will help you stick to your long-term financial goals better than a rigid budget.
Disclaimer: Each individual is faced with a unique financial situation. While this column is intended to be broad enough to apply to everyone, specific investment recommendations and strategies should be tailored to your needs. If you are uncomfortable creating a lifelong financial strategy or selecting your own investments, you should seek out the advice of a financial planner or advisor with a CFP (Certified Financial Planner) and/or CFA (Chartered Financial Analyst) designation to help you.
Financial Planning from 10,000 Feet
Step 1 - Open a brokerage account with a brokerage house like Fidelity or Charles Schwab, and keep your cash savings there. Transfer money into your bank account when you need to pay bills. Brokerage money market accounts almost always offer a higher yield than your bank. Some banks have a brokerage arm, allowing you to link your accounts (such as Bank of America and Citi). 
Step 2 - Eliminate any debt, starting with the highest interest loans you may have. The order is typically credit card, personal loans, business loans, student loans, and a mortgage(s).*
Step 3 - Contribute enough to your employer's 401(k) program to earn the maximum match. If your company matches 50 cents on the dollar up to 5%, you should contribute at least 5%. Check with your employer. Invest as much as possible up to the maximum allowed, if you can afford to do so. Invest in a target-date fund whose date matches your projected date of retirement. The fund will adjust its mix of equity, fixed income, and cash automatically, so you need not worry about the details. Alternatively, invest in a mix of large- and small-cap equity funds, an international fund, and some fixed income. Look for low fees and consistent returns. 
Step 4 - Open a Roth IRA with a brokerage house like Fidelity or Charles Schwab and contribute the maximum amount annually (currently $4,000) per spouse. Use similar investment strategies as in Step 2.
Step 5 - Open a 529 Savings Account and/or a Coverdell for your son or daughter. These accounts have special tax benefits for college savings that make them better investments than taxable accounts or bank savings for the same purpose. Savings Bonds simply will not earn enough interest to exceed the rate of college inflation. 
Step 6 - Seek the help of a qualified fee-based financial planner or advisor. Commissioned brokers and advisors may not have your best interests at heart. You will need help at this point to manage what is becoming a sizable cache of assets, particularly in dealing with tax consequences. They will tell you to do things like buy additional insurance, prepay your mortgage, and begin your estate planning.
*Your mortgage may be in the 5%-6% range, making it worthwhile to focus instead on investing, where you are likely to earn 10% or more annually while incurring reasonable levels of risk.