Ari makes a good point about keeping as little money as possible in low-interest checking accounts. Two follow ups on this.
First, many banks will allow you to provide "overdraft protection" on your checking account, such that savings balances can be automatically transferred to a checking account when needed.
While some banks charge fees for this service, many do not. The only issue you have to watch here is that most savings accounts must comply with federal "Reg D", which requires that no more than six withdrawals a month come out via certain methods (including overdraft protection). If overdraft protection is used only occasionally, this won't be an issue.
Second, you might consider a "rewards checking" account as an alternative to a traditional checking/savings split. If you meet the qualifications for the "rewards rate" in one of these accounts, you'll earn much better rates on your entire balance than you will in a savings account, and you'll never have to worry about any "Reg D" type limits.
An asset management account at a brokerage will also allow a savings-like rate of return on what is essentially a checking account, without the requirements of a rewards checking account. Fidelity and Etrade offer good examples of these accounts, and both of these are referenced on the FiLife web site.