thoughts on this?
I'm not a professional designer, so I wouldn't take this comment too seriously if I were you.
But, from a communications standpoint, an icon is a signifier that resembles what is signified. For example, the icon of a telephone on a phonebooth obviously resembles what can be found inside.
A symbol is an arbitrary signifier for something. For example, $ is a random mark that obviously doesn't look like a dollar.
A logotype, well, duh.
So in my opinion, a logotype is most approriate when the name of the company/product/etc. says what the company/product/etc. does.
An icon works the same way: if you can look at an icon and know what it represents, it could work as a stand alone. For example, Expedia's suitcase icon obviously represents travel.
A symbol is arbitrary and, in my opinion, not be used alone as a logo unless the company/product/etc. is well established. If you see a red "+" then you can assume it stands for the Red Cross, but reverse it and it is the Swiss symbol, make it blue and it's an insurance company, etc...
So to answer in short - it all depends what the logo is for and how it will be used. Are you asking for a specific reason or just curious?
Scott that was an excellent response.
The only thing I could add is If you're deciding WHEN to use an icon with a logo. Has the logo/company been established to the audience prior to seeing any symbols/icons? Is the icon an established symbol that's recognizable by anyone (i.e. to steal Scott's example: a telephone) or is it an uncommon icon developed exclusively for the company/logo (like a concept)? If it's the former, you probably don't need to present the company/logo prior to showing the icon, but if it's the latter; you might need to present the company/logo to create the necessary connections/concept for the icon to become apparent.
Ultimately it's not a cut and dry, do this or do that, solution.