I had just always assumed that mobile phone operators kept a log of every text message you send or receive on your phone. This might not be true.
I had figured that mobile phone operators had been storing the source, destination, and content of the message, as well as the time. This might have been a bit paranoid of me but I basically have never trusted any radio transmission as being secure.
After a Freedom of Information Request made by the ACLU it looks like (at least in 2010) that that may not actually be the case. Turns out that the sheer volume of messages makes storing them impractical (and costly) for most providers. It is estimated by Forester Research that there was 6 BILLION text messages sent a DAY! That is a lot of data, even if you aren’t keeping the content of the message.
Anyway, if you are curious what providers, or if your provider stores your text messages you might want to check out the report found by the ACLU.