Font changes when Cap 9 file is emailed/transferred

Is the output to SWF (where all static text containers are converted to bitmap images) or to HTML (uses CSS)? Do you have dynamic text: this is text with embedded variables. That type of text has to be created on runtime, and in that case you absolutely need to use websafe fonts. Contrary to other applications Captivate doesn't embed fonts by default. You need to tweak the HMTL/CSS files to have this done. Sorry for contradictory information to other comments.

When using fonts, you must be very careful. There are three possible cases

1) in the Captivate authoring environment

the fonts you use here must be installed on your system. If  an external vendor uses a font installed on his system, and then transfer the file to you (whatever the transfer method) the font chosen by the external vendor will be respected in Captivate only if you have it installed too. If not, then Captivate falls back to a default font (such as Arial or Trebuchet, depending on the type of font used - ie serif, sans-serif, etc...)

2) when the project is published in Flash (SWF)

The font used in the authoring environment should be embedded into the .swf file, so you are safe in this case : the font used in the authoring environment is the one used at runtime (because it is part of the .swf file produces by Captivate)

3) When the project is published in HTML 5

In that case, the fonts used at runtime are the fonts installed on the computer of the person taking the course. So if you use a custom font when authoring the project, the students taking the course must have the same font installed on their system when taking the course. This could be possible on a corporate Intranet, but if the Captivate content is to be made public, there is almost NO WAY for a student to have that font installed prior to taking the course. Remember also that a responsive project can only be published in HTML 5, so if your project is responsive, you will run into this issue for sure. If the font used in the content is not available on the student's computer, then, the browser will fall back to a default font.

Solutions

Unfortunately, in Captivate, there is not much to do! The only things you can do are

1. Using Web safe fonts. These are fonts considered safe to use on the Internet because everyone, on every system, will have those fonts. In the Property Inspector of Captivate these fonts are at the top of the list. Don't use a font listed in the "System Fonts" category of the font menu.
2. For content that absolutely need to have  the custom font, use pictures. But that will add some extra weight to your course, so it has a cost in terms of performance and flexibility. 

This is a very common issue for anyone creating content that must be placed online. Web designer and developers also struggle with this. On other Adobe products (such as Muse and Dreamweaver) Adobe now uses a collection of fonts hosted on the Internet. This service is called "Adobe TypeKit". Unfortunately, Typekit is not yet introduced in Captivate. This is definitely one of my topmost feature request for the next version...

I hope it helps.

Are these responsive projects or standard (blank) projects?

Also what version of Captivate are you using?