At the moment i am thinking about buying a new pc because my current one wont run any of the newer games(Oblivion,Fear ect.) that have come out recently,the only thing i'm not sure about though is how i would be able to play WoW with all my existing characters on my new pc,i would like to know if simply re-installing it will work or what will i need to do to get it working and be able to play with all my current characters?
It will work fine just by installing the game on the new machine, it is a client only and will get all the existing information from the server. You can go to any machine that has the wow files on them and log in with your credentials.
If possible copy from you old to your new computer the WTF/addons directory, so u done have to D/L your mods again. Also copy across any files called "savedvariables.lua" in any of the WoW directories.
Thats just so your wow screen layouts are the same as on your old computer.
Just reinstalling the software should work fine - your characters are stored on the server, so they would be unaffected. If you are running any game mods or addons, they would have to be reinstalled as well, but that is not a big deal either, and may not be an issue for you. Good Luck!