Quake3 does not natively support widescreen, however you can setup custom resolutions using the cvars r_customHeight, r_customWidth and r_mode 

Example for 16:9 PAL (UK etc):

seta r_customHeight "576"
seta r_customWidth "720"
seta r_mode "-1"


Example for 16:9 PAL (USA etc):

seta r_customHeight "486"
seta r_customWidth "720"
seta r_mode "-1"

Add the custom resolution settings to a text file called autoexec.cfg in your Quake3 'Base' directory.