Illustrator only likes good fonts
Illustrator likes it when all is OK. That includes a lot of things, but above all fonts. When there's something wrong with fonts, then there's also a probability of crashes. This fonts phenomenon includes the fonts themselves as well as everything connected to them.
As you might have heard, PostScript fonts are dated. Some operating systems already stopped supporting them, which also applies to Photoshop. You shouldn't use PostScript (T1) fonts in your Illustrator projects anymore. Replace them by their up to date OTF versions. Those are in addition cross platform. Replacing them might also lead to changes in text wrapping, since font creators often include a redesign when updating a font.
Fonts are software and your computer does a lor of read operations with them. The files can corrupt. In my own memory this happened more often with PostScript fonts than with TrueType or OTF fonts. THis might also be due to better quality hard disks.
Check your fonts, when you suspect them to cause you issues. On Mac OS you can use Font Book for that. Find the command in File > Check font.
Duplicates might also cause you trouble. Because Mac OS has so many font folders, you might install a duplicate in a different font folder by accident.
Besides being a cause for crashes, corrupt fonts also might just be unavailable in applications such as Illustrator. In Windows it's also possible to install a font in the wrong way. In order to be available in Illustrator, you need to install them "For all users". Select the command from the context menu when right-clicking the font file.
A corrupt font cache might also lead to trouble. There are a lot of help pages on the Adobe website about font troubleshooting. Soe of them quite old, but there can still be clues in them.
Unfortunately besides the fonts managing fonts is also problem-laden. Of course Suitcase, FontExplorer et al are a convenient way to load fonts on the fly when opening a document. But the font management app needs to match the Illustrator version exactly and needs to be fully compatible. Still there might be issues. For a lot of users font management just works. Others experience problems upon problems.
The good thing ist: you don't need font management, in order to just install fonts. All you need to know is where they belong. On the Mac there are several font folders.
User ~/Library/Fonts/ Each user has complete control over the fonts installed in their Home. These fonts are available to that user when he or she is logged in to the computer. Fonts installed here are not available to all users of the computer.
Local /Library/Fonts/ Any local user of the computer can use fonts installed in this folder. Mac OS X does not require these additional fonts for system operation. An admin user can modify the contents of this folder. This is the recommended location for fonts that are shared among applications.
System /System/Library/Fonts/ Mac OS X requires fonts in this folder for system use and displays. They should not be manually altered or removed.
Long article about Fonts on Mac OS in case you want to dive very deep.
In order to install a font, you go to the appropriate folder and move or copy the font into it. If you copy it, you always keep a backup of the file and also in order to uninstall it you can just delete it from the folder. Illustrator doesn't need to be restarted.
In order to open your user library, while in the Finder press the Alt key and open the menu Go to > Library. The Fonts folder is inside.
Image: By default Mac OS is set up in a way that the Library is hidden. To show it in the menu you have to press the Alt key.
Font Book also works for a lot of users (in newer system and Illustrator versions). If you don't want to install and deinstall fonts manually, try Font Book and see if it works for you (documentation on the Apple web site).
Install fonts on Windows
On Windows you right-click the font file and select "Install for all users" from the context menu. If you install fonts just in your account, then Illustrator might not find them and thus not list them in the menu.
Too many Fonts (is that even possible?)
You also shouldn't overload the font menu, since all fonts need to be loaded into your computer's RAM. And they also strain Illustrator. You can uninstall them the same way you installed them: open the folder and delete them from there.
System fonts shouldn't be deleted. The system itself and several applications need them – even the forein ones. A couple of Illustrator versions depend on some default fonts such as Verdana and Tahoma in order to correctly display the user interface.
More tipps and tricks concerning fonts in Illustrator 1 2 (in German)