I think that this is a question where the answer changes depending on the age of the "extra" and where they are in their career.
If you are an adult actor I think the answer is unequivocal (hang on, I can't
think it's unequivocal can I

- it's comfortable here on this fence though).
If you are an adult actor, and wish to be taken seriously as an adult actor,
don't do extra work OR do it quietly/under another name if you can and keep your head down. Treat it as a money-earning job like working as a waiter or stacking shelves and never, ever put it on your acting CV.
http://www.youtube.com/watch?v=lvBvXMZZ ... re=related
The only exception I can think of is if you are at the very start of your career and you would like to find out what is like to be on a film or TV set, in which case you should still keep your head down and keep a low profile.
There honestly is a very clear divide in this country and SA's (supporting artistes) are treated and regarded differently from guest artistes who have one line. I don't think this is fair or appropriate, but it is the case.
If it is a child, I think it's different. I would still say that you should not include any background credits on a CV. You can, however, emphasise the positive experience to a prospective agent in a covering letter because there are lots of positives:
It shows that the child has
1) An ability to cope with lots of waiting around
2) An ability to behave responsibly on set
3) An understanding of what goes on in a film/TV environment
as long as you make it clear that you don't regard it in the same light as a credited experience I would think an agent would see the positive side of this experience.
So, make the most of the positive experiences, but don't crow about them and don't expect anyone in the industry to regard it in the same light as being employed as an actor.
As an extra, you don't (generally) get hired in the same way as an actor does. As an extra you are generally picked as reasonable wallpaper because you come into the required "mix" - 3 student types, 3 businessmen, 1 old lady, 5 children making their way home from school. As an actor, you are generally chosen by audition or by showreel because of your ability (though obviously "looking the part" still has a big influence on whether or not you get picked).