This list is currently what some people call "best of breed"; there are alternatives listed at the end of each option.
of course if you're a windows user wanting to explore open source software then you may wish to examine OpenDisc, a collection of "best of breed" OSS for win32.
This page needs an overhaul. I tried various formats, including a table based, but they all suck; the current form is not very good either, but the least bad of all I tried in my opinion.
There are both GNOME and KDE options listed (why - this distinction is unnecessary, and could confuse/distract newbies), but remember, you can run programs from one toolkit on the other DesktopEnvironment if you have the right libraries installed. Remember also, that lots of Linux software gets ported to MicrosoftWindows too.
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.
zcat(1) suggests a "free on windows" v. "non-free on windows" list too, either here or on a new page. Eg Mozilla / opera / gimp / mplayer / xmms all have windows versions, which can be used as replacements for IE / OE / Photoshop / WMP / Winamp Please don't make general comments on this page; edit or create a page for the package in question with your comments.
Except for Konqueror, all of these are also available for MicrosoftWindows. You probably want Mozilla even there. Opera is commercially distributed, but has a free version which shows you banner ads. Lynx, Links? and w3m? are console clients; Lynx is available practically everywhere, while the other two do a better job of "rendering" pages; Links? is menu driven and therefor easier to learn.
Use Evolution if you need a MicrosoftOutlook clone (including calendaring, task management and an RDF news aggregator). Otherwise, MozillaMail is a popular client with some very advanced features such as bayesian spam filtering; it will be superceded by MozillaThunderbird (also known as IceDove?). Mutt is a stunningly powerful client for the console inclined, while Gnus is similarly appealing to the Emacs populace.
AbiWord is well integrated into GNOME and very lean. If you don't need a full Office suite replacement, it is probably a better choice than OpenOffice.org Writer. For KDE users, the KOffice project provides a !FrameMaker?-like desktop publisher/word processor called KWord.
LaTeX uses a completely different approach, which is not dependent on any GUI application. Rather you write your document as a plaintext file with markup, which can be done in the editor of your choosing (Emacs has a very cool LaTeX mode). This file is then fed to an industrial strength typesetting engine and usually output as PostScript or PDF. LaTeX is not good at very freeform layouts such as fliers, but excels at standardized layouts such as books, reports, or business letters. It is very well worth a look, particularly if you deal with large documents or high volumes of correspondence.
If you're not already working with OpenOffice.org or KOffice, you want Gnumeric (a project started by GNOME founder MiguelDeIcaza). It supports all the functions that Excel does and then some, has good import filters for Excel sheets and just as pleasant an interface.
Noatun and XMMS are much like WinAmp, even skin compatible with it if you haven't gotten over skinning. If you prefer the 'music list driven' interface inspired by Apple's iTunes, check out RhythmBox.