First of all -in the US- font designs are not protected by copyright. Digital fonts do enjoy copyright protection over the actual data they contain, and a small number of fonts are protected by a design patent, but technically -if not ethically- you can make a knock-off of almost any existing design.

The thing is, you don't need to worry about any of that if you're simply using a font*: you would purchase a license to use it, and that's that. It's only if you're making a font of your own based on an existing one (or if you're redistributing somebody else's font) that you have to worry about legal/ethical issues.

* There are some exceptions however, in that some font houses require extra payment for certain uses.

hhp

There is no difference between a Bodoni and, say, Minion, because they are both (in their digital versions) recent fonts created by specific designers. It doesn't matter that one of them is directly based on a previous font and one isn't. Which is to say, if you are talking about digital fonts, none of them are "rather old typefaces."

As Hrant says, typefaces are not copyrightable in the US, but you do need to buy a license from the type foundry in order to use them. With some exceptions, that single license is all you need to use the font on any product, unless the type itself is really the relevant part of what you are selling (like decorative pillows with monograms in a certain typeface). In cases like that, some foundries will need extra compensation, because their font is essentially the only notable attribute of your product.

But no one is going to sue you for using a font, as long as you obey the foundry's EULA.

The original design of Bodoni and Clarendon (but not yet Univers, right?) is royalty free, but just the “design”. Digital fonts based on the design are not, neither is original lead type or lead type based on the original design by their physical nature.

The place you buy the font from will determine how you can use the font, and you'll find details in the licence agreement (EULA) that comes with the font. There shouldn't be any grey area: the EULA is a legal document.

Another option is to use "Libre" fonts (The ones released under the SIL Open font license).

Libre fonts allows you to use them for personal and commercial projects alike.
You can find lots of Libre fonts at Google Webfonts and the Open Font Library
http://www.google.com/webfonts
http://openfontlibrary.org/