(updated 2011-nov-23)
In short: Most likely. I’ll get right to the point and list some application alternatives (to what you find on the two major commercial alternatives to Linux; Apple’s Mac OS X and Microsoft’s Windows) I either use myself, or recommend to those who need such functionality.
Task – App on Mac or Windows – App on Linux
– Communication
Web browsing – Safari, Internet Explorer – Firefox/IceDove, Galeon, Konqueror
eMail – (Apple) Mail, Windows Mail - Thunderbird, Evolution
File Transfer via FTP – Transmit, Fetch – gFTP, FileZilla
Bittorrent File Transfers – Azureus, Transmission, uTorrent - Azureus, Transmission, Deluge
P2P downloading and sharing – Shareaza – aMule
IRC chat – Snak, mIRC – Xchat
Instant messenging (IM) – iChat, Adium – Pidgin, Empathy (or Skype, which is availabel for all, but not open software)
Remote Desktop (VNC) – Apple Remote Desktop – vino, vinagre
– Office and Productivity
Calendaring – iCal, Outlook – Evolution, Sunbird, Lightning for ThunderBird
Office Apps – Pages, Numbers, Microsoft Office – LibreOffice, AbiWord, GNUmeric
Anti-Virus (if needed) – too many to mention
– Xclam
– Other productivity apps
Graphics Editing – Photoshop (professional) – Gimp
Vector Graphics - Illustrator (professional), Corel draw – Inkscape
3D rendering - AutoDesk 3DS Max, Lightwave – Blender
Music composing – Garageband – Rosegarden
Advanced Text Editing & Programming – TextMate, UltraEdit – Geany, XeMacs, Vim (and really, really many others)
IDE / Programming Environment – erm, various – Eclipse, NetBeans
– Utility functions and Media
Editing Text files - Textedit, Notepad, WordPad – gedit
Graphics viewer - Preview -EyeofGnome, GnomeViewer
Video editing – iMovie, Windows Movie Maker – Cinelerra
Video playback – Quicktime Player, Windows Media Player – VLC, Totem
Photo Cataloguing – iPhoto – F-spot, ShotWell
Music Cataloguing and playback – iTunes – Audacious, Banshee, Rhytmbox (and yes, it does work with your iPod)
– Other
Virtual Environments for software – Parallels, VMWare - Virtualbox OSE
.NET programming environment - Mono
For running largely *any* Windows app, you have Wine, The Windows Environment.
For any kind of web (apache), data (ftpd) or database hosting (mysql), Linux or other UNIX derivatives like it are basically the best solution for getting the job done; Unix machiens have been the backbone of the internet since its childhood. If stuff like this is what you need to do, you should look to a Server edition (fx. Ubuntu Server) of whatever Linux flavor you’re reading up on.
This is a cursory list of the things people do with their PC’s today. Obviously I can’t cover all tasks and jobs you need for your computer for, and if it’s not on this list, it does not mean that Linux can’t do what you’re looking for, merely that I’ve either not thought about that particular app, or that I’m too lazy to type it in. After two years with Linux as my OS of choice, I’ll say as much that I’m of the opinion that if there somethign you can’t do on Linux, it’s probably not worth bothering with. (Games? Get a console, PC’s are for serious business. Yes.)