In school I was always told to say "je voudrais", as it is much more polite. I have been living in Paris since last year, and I have had a lot of friends (especially in the restaurant business) tell me that politeness has become rather old-fashioned. People have become much more demanding, and you do hear "je veux" much more often... Blame the tourists...?
As far as personal preference though, I would rather take the polite version any day :)
I translated it as "I would like..." and got it wrong. "I want..." seems a little coarse (in British English, at least!) I think I would always prefer "voudrais" over "vieux" when asking for something. I've heard other English speakers in restaurants say "I'll have..." or even "I'll get..."