Currently, the help for text searches has the following...

Note: The NOT operator cannot be used with just one term. For example, the following search will return no results:

NOT "atlassian jira"

For reference:
http://www.atlassian.com/software/jira/docs/v3.6.4/querysyntax.html?clicked=jirahelp

Many times I could really utilize a search that would exclude a word or a phrase. There doesn't seem to be any way around this, and it's frustrating.