If you have large savings, the amount that you can make from bank bonuses may not be enough to matter. However, for savings balances around $10K, bank bonuses can be significant. For example, if you have $10K in a savings account with a 1.00% rate, you'll earn about $100 over a year. With many bonuses, you can earn $100 soon after you open an account.
The bank best known for its new-account bonuses is Chase Bank. They have long offered $100 checking account bonuses. Unlike interest rates, bonus amounts have gone up. In the last year, a $150 checking account bonus has been made available online at Chase. Here's a Chase promo link for the latest $150 checking bonus. This one is scheduled to expire on
2/15/2012 (new expiration: 5/15/2012). This requires a new Chase Total Checking account with direct deposit, and it's only available for new Chase checking customers.
Chase also has a $200 business checking account bonus that's available at this promo page (credit to iBankDesign markber for this find). This promotion is scheduled to end today (1/31/2012). However, this is another common bonus that I'm sure we'll see come back.
Not all Chase bonuses are online. Chase often mails targeted bonuses to customers. Chase recently mailed me a $100 offer for opening a new savings account with an opening deposit of $10,000 or more of new money. The promotion doesn't require that the $10K balance be maintained. As you might expect, the savings account rate is very low so you won't want to keep a large balance in this account.
As I described in this post from last year, bonuses may be larger, but you have to be more careful to avoid monthly fees. All of Chase checking and savings accounts have monthly service fees. Most can be avoided if you meet certain requirements such as minimum balance or direct deposit.
Other Bank Bonuses
We have a bank promotions page with a table of all of the active bank and credit union promotions. You can filter the table based on the type of promotion and based on your state. I have more details about how to use this page in this blog post.