I only store bitcoins offline. I send money to MtGox or other exchanges in small amounts, and only for the length of time it takes to make a transaction and get my money out again.

You may choose to trust an online wallet service if you feel they are trustworthy. I will not trust ANY online wallet until bitcoins can be stored safely even when a hacker has complete access to them. For instance, if bitcoins could be marked as savings in the protocol and become non-transferable for a period of time selected by their owner.