There are a few ways of recording phone calls — Skype, a third-party jailbreak app on your iPhone, a digital voice recorder with a headphone adaptor — but none have been as easy as using TheInterviewr. The web app lets you schedule interviews, upload documents you'll use for that interview, and, best of all, record it automatically.
TheInterviewr calls you first, then you pick up, and then it calls your interviewee and connects you two seamlessly. The recording starts immediately, without any voice prompt from the service, so the onus is on you to make it known that you're recording the conversation, because surreptitiously recording phone calls is illegal. If you're interviewing somebody, however, it's usually assumed that you're going to record the call for transcription reasons. Once you're done with the conversation, you click a button on the webpage and it automatically generates an MP3 for download.
Although its main use is recording interviews, you could easily use this service for recording customer support calls, calls that you want to save for posterity, and calls that you want documentation on for legal reasons. Again, check your local state laws for phone recording, because some require only one party's consent for recording (that's you), while others require both party's consent.
Signup is free, as is the service itself, but they've stated that they're going to look at monetizing in the future, while keeping the no-cost price tag.