I am sure that a lot of you have heard of the "Keep the Change" program offered by Bank of America. Essentially, they round up your check card purchases and place the extra funds into a savings account. In addition, they match this change up to $250 annually. They match it at 100% for the first three months the account is open and at 5% thereafter. Overall, this is not a bad deal. But, if you work it all out right, it can be a much better proposition.
Bank of America also offers sign up bonuses, and they are frequently detailed on the Fat Wallet Forums. Right now, it appears that it is $125 in sign up bonuses. Open a free checking and a savings account, and then enroll them in the "Keep the Change" program. In addition, there are talks about milking "Keep the Change" so that you max out your $250 in the first three months, so that you don't have to worry about it the rest of the year. So, $125 plus the $250 match and your $250 contribution add up to $625 in savings, very nice.
There are further exploits outlined on the Fat Wallet Forums that discuss the ability to open many accounts, and you can receive the sign up bonuses and enroll in "Keep the Change" in each. So, you and a spouse/partner could each sign up for this program... and given what seems to be a 90-day waiting period, you could each do this four times a year. $5000, cha-ching.
At one time, Bank of America was also offering $10 to $15 for using online bill pay. You could do this with each account, likely, and add another $80 to $120 for the entire year.
Certainly, you could go overboard with this. But, if you just want to get started, go open up an account and make sure to use the sign up bonus. Then, enroll in "Keep the Change" and start saving. Also, make sure that you evaluate the different types of accounts and pick the most appropriate. There are fees and minimum balances that vary for each type. "Keep the Change" is supposed to work with any checking/savings account combination.