1) AIM replacement
2) MSN messenger replacement
3) media player w/skinnable interface
4) C++ and Java IDEs, preferable with interfaces similar to NetBeans or Visual Studio .NET (I read somewhere that either IBM or Intel, forgot which, has one for Linux)
5) PDF reader (the PDF Viewer prog that comes with Red Hat doesn't do the job adequately)
6) file sharing program
7) Minesweeper
8 pinball
9) syncing program for a PDA (iPaq, not Palm) (This might be a tough one since it's running a compact version of Windows...)

Also, I don't suppose it's possible to play my games in Linux (the ones that require MS's DirectX)?

1) & 2) gaim (gaim.sourceforge.net)
3) Mplayer (http://www.mplayerhq.hu/homepage/), Kaffeine (KDE Xine interface, http://kaffeine.sourceforge.net/), Xine (http://www.xinehq.de)
4) IBM has Websphere Application Developer but it is expensive and I don't think there is a free version, kdeveloper + qtdeveloper is pretty good for C++/qt apps.
5) Acrobat Reader (www.acrobat.com)
6) SSH (scp/sftp), Samba (SMB Windows Networking)
7), 8), 9) Sorry, no idea, but hopefully something above was helpful.

Sorry, missed that last bit. Check out www.transgaming.com for information on DirectX based games under Linux. They make a product called WineX that allows you to play some games. They have a nice big directory of what games are supported.

Yep, those were really helpful. Thanks for the tips. And I just realized that I already have KDE's version of Minesweeper on my box, so that takes care of that.

4) There is netbeans for linux. You could also try out eclipse.

7) There is a minesweeper clone both in kde and gnome. I don't remember their names, but check it out in the games menu.

Oh, I almost forgot:

10) download manager that will allow you to resume downloads

i think wget can take care of that