You can freely use all types of fonts (TrueType, TTF ...)! FALSE No, you can't.
Like any artwork, the author of a font must be paid for his work. This is important work, which is far from being trivial:
Apple paid a lot to create a particular font: The "Apple Garamond" (based on the Adobe Garamond).
Microsoft create special fonts (Trebuchet MS, Times New Roman, etc..) for its products (Windows, Office,...).
There are many companies that are involved in the creation and sales of fonts: Adobe, Monotype, Linotype, etc.. and a large number of artists who sell their creations directly (Ray Larabie, etc..)
To use a font in one of your publications, you need to buy the rights from the author.
The vast majority of fonts used on many websites (like DaFont) are not free. They are being used illegally (but it is difficult to sort out).
There are several solutions available:
Clones of the most popular fonts exist.
Make use of a free font.
DejaVu: Family of free fonts, supporting international characters.
Free Font Manifesto: A group of typographers who have decided to give some of their fonts (hundreds of free fonts from Manfred Klein).
Open Font Library: A site that lists the fonts with free licenses.
Misprinted Type: Some free font.
UCS Free Fonts: Clones of popular fonts
Ray Larabie: The typographer distribute freely his work, but for download, it is compulsory to register at myfontom.
WC Fonts, French community distributing some free fonts.
Read the license associated to these fonts: They are free but some can only be used under certain conditions (For example Manfred Klein: Free for non-commercial use and for commercial uses, it is mandatory to make a donation to NGOs). If you use a font in an image, a Flash movie or a PDF document, you must pay the license for its use (which is not the case when using a font for your HTML, CSS coding).
Thanks to Sebsauvage for this tip