Dear Shy in Vancouver,
You don't say whether you are a man or a woman, but my advice is the same either way. Acting and modeling are two jobs which at some point may require some nudity, but it's up to you as to whether you are comfortable with the roles that require this.
It's important to remember that most actors have been in nude scenes at some point in their careers, and also that if you are uncomfortable you can always say no. Ok, so the director may find someone else to play the role. It's a choice that many actors make. Actresses like Sarah Michelle Gellar and Jessica Alba have no nudity clauses written into their contracts. Sometimes someone will say something like "You only get to make those decisions when you are a big star" in which case you know that they are being cynical and manipulative and you can make the choice to walk away.
Yes, there are sleazy directors. In which case don't work for them unless you are happy to be part of their game. Lots of actors and actresses make bad decisions in an effort to get some work or open up an opportunity along the way that catch up with them. Should we judge them for it?
Censorship, shock factor ... It's easy to get puritanical about nudity. In the 60's it was mostly women getting nude on camera. In this day and age anything goes and there are plenty of men happy to take it all off. It's not just men's torsos on display either; full frontal nudity has become more acceptable for both sexes. It's also not just a case where people with perfect bodies are getting naked.
Is nudity required for the drama to be successful? Does nudity change the dynamic? Is it the right dynamic? For instance, The Watchmen raised the bar for comic book visual accuracy with it's no blinking portrayal of Dr Manhattan's nudity. Some viewers who hadn't read the Graphic Novel were shocked at how 'adult' this film was, perhaps expecting something more mainstream. Others were pleased that the director stayed true to his source material and the character. It is necessary to show Dr. Manhattan nude. It communicates an essential part of his invulnerability and his obliviousness to others. Therefore it is a valid artistic decision in the Graphic Novel and in the film.
Talk to your director about your feelings. It is his or her job to make you as comfortable and supported as you need to be to do your job. Many "actors" are attention seekers of the worst sort and will drop their pants at a moments notice. Sometimes nudity is just there for the shock factor, especially in student productions, and often in this case you can certainly negotiate wearing some clothing!
If it is a professional production, you may not be able to negotiate. If you are shy about this and wish to continue to be an actor you should consider the reasons for your shyness very carefully. Acting asks us to examine our own internal life and to identify with and understand the internal life of other people. Shyness does not really have a part in your actor's life; it will inhibit your ability to do good work. Don't confuse shyness with being well mannered.
At the end of the day, it's got to be your choice and something you feel happy doing. Base your decision on where you are in your development as an actor and what the material requires. If it makes you feel cheap, don't do it. If you can do it and feel confident, more power to you!