This is a very interesting question, because it turns out that the laws on recording phone conversations are different depending on the location of both the caller and recipient of the call. There's a splendid informational site run by the Reporters Committee for Freedom of the Press wherein they explain:

"Federal law allows recording of phone calls and other electronic communications with the consent of at least one party to the call. A majority of the states and territories have adopted wiretapping laws based on the federal law, although most also have extended the law to cover in-person conversations. Thirty-eight states and the District of Columbia permit individuals to record conversations to which they are a party without informing the other parties that they are doing so. These laws are referred to as "one-party consent" statutes, and as long as you are a party to the conversation, it is legal for you to record it."

They continue:

"Twelve states require, under most circumstances, the consent of all parties to a conversation. Those jurisdictions are California, Connecticut, Florida, Illinois, Maryland, Massachusetts, Michigan, Montana, Nevada, New Hampshire, Pennsylvania and Washington."

The most important information on the site is that they highlight that it is definitely illegal for you to record a conversation without consent of either party (e.g., if you were to record the conversation between your salesperson and a vendor without either knowing about it).

On the other hand, if you're on the phone and you consent to taping yourself, you're good, as long as the other party isn't in one of the twelve all-party-consent states. Until I did the research to learn more about this particular problem, I also didn't realize that one-party consent was sufficient for this sort of thing, so in most cases you would indeed be able to legally record any and all conversations you had with your vendors.

I'm based in Colorado, for example, and according to Colorado statute one-party consent is sufficient. The penalty, however, for recording a call without the consent of either party is rather serious:

"Colo. Rev. Stat. 18-9-303: Recording or overhearing a telephone conversation, or any electronic communication, without the consent of a party to the conversation is a felony punishable by a fine of between $1,000 and $100,000 and one year to 18 months in jail."

Y]ou definitely want to ensure that it's legal so you don't get into serious hot water, but for most states of the United States, it appears you'd be in the clear.

Let me just add one additional thought: if you're having problems with salespeople offering one deal via phone and another when the bill comes in, it sounds like your ultimate solution is to pin them down in specific contracts or letters of intent, not to record those phone conversations. It should be easy to turn around to a salesperson after a particularly engaging phone call and say "Sounds great. Draw up a quick contract, fax it to me, and we'll get the order in!" If they won't put it on paper, then I would find a new supplier or service bureau. Something to think about.