Currenty I am running DNN 4.4.0. I have never turned on the compression. Is it safe to turn on the compression, and what should be the highest setting?

It's safe as long as you configure it properly.

Curiously DotNetNuke.com is still running without compression though, so maybe it is giving them trouble.

There were some initial problems with compression when it was introduced in 4.4.0.

However, 4.5.0 introduced some significant changes so that it would work more relaiably.

These are documented in Gemini issues DNN-5004 and DNN-5125

The changes are as follows:

1. Only Default.aspx is compressed - As 99% of all pages are Default.aspx - this avoids the need to exclude paths for aspx pages that shouldn't be compressed (line LinkClick).
2. Only text/html MimeTypes are compressed - Again as compression is only really neccessary with text pages this avoids the need to configure excluded mimetypes

As far as I know (there have been no posts since 4.5.0 was released) these changes have solved all the issues people were having.

Note: while Default.aspx is the only page compressed - specific tabs can still be excluded by using "tabid=xx" in the excluded path.