Can I send bitcoins with my mobile phone? Is it possible to send and receive bitcoins with a mobile phone? If so, are there bitcoin clients for Android or iOS?
There are at least two actual clients for Android and half a dozen "thin clients" that connect to a bitcoin server at home. As the thin clients are kind of complicated installs, I recommend Bitcoin Wallet by Andreas Schildbach. 
There are a few questions of security as both apps have no way (that I'm aware of) to import/export/backup wallets and it's uncertain what level of security is held on data Google keeps in the cloud, but for carrying a small amount of coin for daily use, both are viable options.

Not being an iOS person I can't weigh in on the features etc. of the various iOS apps, but a quick glance over the various projects seems to show an assortment of thin clients and no actual iOS-based bitcoind implementation.