Ahh, the dreaded scope creep. (Actually I kind of like "brief creep." At the risk of saying the wrong thing, it sounds a little like getting a wedgie, and the actual situation is just about that uncomfortable... ;} }
It's a function of project management and cost containment vs. giving excellent service.
Let's say I am a premiere Web designer, and you have engaged me to design a site for your company. We have taken care of all of the preliminary discovery. I have presented you with a document (in my own case, it would be a statement of work) including detailed specifics on the number of pages, what is to be included (forms, Flash design, photographs, maybe an e-commerce interface, whatever). I have also provided you with an accurate, good-faith estimate of the number of hours it will take to complete this work. You, the customer, have signed off on this, so we have a legal agreement--a contract for the work. You are aware of, and have agreed to, the fact that the hours section is an estimate only, and that you will be billed for the actual hours worked. You've made a deposit.
Now we are into it. I have created the actual design and layout of the pages, and you like and approve of it. (If I'm smart, I'll present this to you and get you to sign a memorandum of approval--a sign-off). Things are rolling merrily along, when you call me up one day. "Gee, Anne, the site design is looking great. But I've been thinking... I'd really like to have a Flash intro for the site. Something achingly trendy."
This should trigger an alarm. It is a change in the scope of the contract. It's going to take me several hours to develop that screen, and there will need to be modifications to the rest of the pages as well. As the designer, I'm now squarely in a dilemma. I want to give the best possible service. I want referrals and repeat business. But I also need to eat.
How to handle it? I should immediately say, "That's a great idea, Mr. Client. It'll probably take me eight additional hours to get that done for you. I'll just write up a change order and get it to you for your approval, and then we can get right to work on it."
In practice, this is easier said than done. If I haven't prepared you for change control, you're apt to throw a fit. There's a bit of risk. Maybe you'll get angry and stop the work and tell all your associates I'm a gouging, mercenary creep. Maybe I'll back down and decide to inclue the work in the original price, thereby losing eight perfectly good, billable hours. Ugh.
The best way to handle it is from the very beginning. Be frank and open about change control in your discussions, and include a paragraph covering it in your statement of work. Include checkpoints in the work--natural stopping places where the client will have opportunity for review and approval. Build time in for those necessary, legitimate revisions that will be inevitable. Report to your client on your progress as you go along.
Having done all that, a change in scope doesn't have to be quite as scary. The other lesson to be learned out of this is never to work without a written agreement.
I'm certain there are other approaches to this. I've been a network engineer for twenty years, a Web designer for less than a year. So most of what I've written here is based on that other consultancy. But I think it translates pretty well, and it's done OK for me so far.

Hope this answer isn't too long-winded!!
Anne