<p>I want to make some passages of a standard tooltip bold in a WinForms application. Is this possible?</p>

<p>If not, is there a (free) tooltip component that allows me to style them (preferably also border and background)?</p>

<p>Thanks!</p>

You can use this type :
Balloon tool tip
. This let you have some bold title and some color option. You might be able to modify the source to get underline, italic and bold inside the message.
Update:
You can modify the drawing of the ToolTip (and the FONT object of the text).
This is how to do it
. The code in this link is for the normal ToolTip, not the Balloon I posted above.