See also the more heated WhatSoftwareDoPeopleUse.
Remember, lots of Linux software gets ported to MicrosoftWindows too.
This list is currently what some people call "best of breed"; there are alternatives listed at the end of each option.
Another important point is that these equivalents are likely to provide you the easiest transition. Once you get into the UnixWay, you might want to do things differently; perhaps you might want to start using console applications. However, the list here are most likely to be useful to YourMum, as edited by consensus.
There are both GNOME and KDE options listed, but remember, you can run programs from one toolkit on the other DesktopEnvironment if you have the right libraries installed.
Please don't make general comments on this page; edit or create a page for the package in question with your comments.
Internet Browser
Mozilla1? is quite clearly established as the internet browser to beat. It aims for standards compliance, and has popular new features such as tabbed browsing and popup blocking. Galeon is a GNOME browser that uses the Mozilla rendering engine Gecko. (Learn more at MozillaNotes).
Konqueror's rendering engine KHTML is the basis for MacOSX's new Safari browser.
Opera is a pay browser. (There is a demonstration version that shows you constant banner ads, if you can live with that.)
Lynx and Links are text mode clients. Links is newer, menu driven, faster, easier to navigate, and renders multi-column text better than Lynx.
E-Mail Client
Ximian's Evolution client is very much a reimplementation of OutlookExpress's big brother MicrosoftOutlook. As well as email, it offers calendaring, task management and a RDF news aggregator.
If you go for the console, there's a very powerful mail client called Mutt.
Mozilla Mail1? is quite popular and has some very advanced features such as bayesian spam filtering.
Word Processor
While OpenOffice.org is a 'full Office replacement', !AbiSource?'s !AbiWord is better integrated into GNOME. If you are a KDE user, the KOffice project provides a !FrameMaker?-like desktop publisher/word processor called KWord.
If you want to do serious reporting or document writing, look into LaTex?. You'll be glad you did. (It is a markup language like HTML, but complex and with an unusal yet powerful syntax.)
Spreadsheet
Gnumeric, a project started by GNOME founder MiguelDeIcaza, supports all the functions that Excel does, and even some more. It might suit you more than OpenOffice.
Presentation Program
Music Player
Skin compatible with Winamp. If you haven't gotten over skinning. :)
If you prefer the 'music list driven' interface, check out RhythmBox.
Video Player
These days media players are converging; you can play mp3s and DivX etc with the same program.
1? Mozilla is also available for Windows and MacOS.
See also A Windows Guy Tackles Linux and
The table of equivalents/analogs for Windows software on Linux
No page links to LinuxEquivalentsForWindowsSoftware.