In addition to the many different modes available for Emacs, there are also many add-on packages. I call them packages because they're more than just new modes. They often include extra utilities or are so large that calling them modes just doesn't seem to do them justice. In still other cases, they are software which extends or integrates other Emacs modes and packages. The distinction isn't entirely clear, but that's okay.
To quote the VM FAQ:
VM (View Mail) is an Emacs subsystem that allows mail to be read and disposed of within Emacs. Commands exist to do the normal things expected of a mail user agent, such as generating replies, saving messages to folders, deleting messages and so on. There are other more advanced commands that do tasks like bursting and creating digests, message forwarding, and organizing message presentation according to various criteria.
When I first began using Emacs, I tried VM out for a while. I found it to be a great replacement for Pine, Elm, or most any other mail program. But I didn't want to use separate programs to read mail and news. VM is actively developed and well supported today.
It is available here: http://www.wonderworks.com/vm/.
To quote the GNUS Manual:
Gnus is a message-reading laboratory. It will let you look at just about anything as if it were a newsgroup. You can read mail with it, you can browse directories with it, you can ftp with it---you can even read news with it!
Gnus tries to empower people who read news the same way Emacs empowers people who edit text. Gnus sets no limits to what the user should be allowed to do. Users are encouraged to extend Gnus to make it behave like they want it to behave. A program should not control people; people should be empowered to do what they want by using (or abusing) the program.
GNUS is what I currently use for mail and news (as hinted above). GNUS is also actively developed and well supported today.
It is available here: http://www.gnus.org/.
BBDB is an Insidious Big Brother Database, a rolodex-like program for Emacs that works with most of the popular Emacs Mail packages (VM and GNUS included).
It is available here: http://pweb.netcom.com/~simmonmt/bbdb/index.html.
AucTeX is another mode for editing TeX files.
To quote the AucTeX web site:
AUC TeX is an extensible package that supports writing and formatting TeX files for most variants of GNU Emacs. Many different macro packages are supported, including AMS TeX, LaTeX, and TeXinfo.
It is available here: http://sunsite.auc.dk/auctex/.