It depends on the software.
Most tracking software can show you visitors that came from web-based email providers such as yahoo email or AOL web email. But most web analytics software cannot read and track visitors from email clients such as Outlook and Eudora and simply lumps these visitors as Others (or however the web analytics software defines it to be)
There are however some web tracking software that can tell you if the visitor comes from an email marketing campaign,
Google Analytics, for example, allows you to track if the visitor comes from an email marketing campaign — IF you actually put a tracking code in the emails that you sent. http://www.google.com/support/googleanalytics/bin/answer.py?answer=55540&query=email+campaign&topic=&type=