when you are in Outlook Express, just click FILE and SAVE AS,...then decide .where you want it,....and if you want it to be an .".eml" ( actual e-mail file) or just a".txt" ( plain text file), by using the drop down window ( SAVE AS TYPE )
if you just want to save the body of each message for future reading, I would use "text" and use notepad to open them later....quickest way anyway.
if you want to keep all the "to" and "from" info ( header ) ,etc,....then save as an e-mail file and it'll open as such when you click on it later
In Hotmail, I would just copy and paste the text to a notepad file on my desktop, but you could click on the words ( PRINTER FRIENDLY VERSION) just above the message body and then hit (ctrl + A) to highlite everything, then right click...save as....etc.....this way will keep all the header information for you, for future reference