The list of fonts you actually need to know is the list of the web safe fonts.
The reason is that, when a mail client like Outlook, Thunderbird, or Mail on OS X or iOS displays an HTML mail message, it uses some well-established HTML layout engine. For example, Thunderbird uses the same layout engine used by Firefox, which is Gecko, and Mail uses WebKit, which is the one that renders HTML pages in Safari and Chrome.
Below is the list of web safe fonts recommended to be relied upon by w3schools.com:
- Palatino Linotype
- Times New Roman
- Arial Black (not available on iOS 5)
- Comic Sans MS (not available on iOS 5)
- Impact (not available on iOS 5)
- Lucida Sans Unicode (not available on iOS 5)
- Tahoma (not available on iOS 5)
- Trebuchet MS
- Courier New
- Lucida Console
Alternative lists of web safe fonts:
Common fonts to all versions of Windows & Mac equivalents
Safe web fonts
More information: Web typography
As for iOS in particular, you can check what fonts are installed on an iOS device using Typefaces app, which is free, or using this online tool.