If you're leaving your current employer, there's obviously some reason. In any situation, your best bet is going to be to outline those reasons and state that those are what are motivating you towards accepting the new position. The key here is you need to be specific, rather than giving vague reasons like 'the new opportunity will be better for my career'. If you can give them a concise set of points, and the company knows they can't offer you the same thing, a good company will wish you luck and let you know to keep them in mind if the new position turns out to not be everything you thought it was. If you give them a vague statement about career opportunity, the company will come back with a title change and/or salary increase and continue to pressure you about staying.
If the reason you're leaving is for more interesting projects and career advancement, you have to tell them that. Tell them where you envision yourself in 5 years, and highlight how the new position will help you get there. If they come back with a salary increase as their counter-offer, you can tell them that you appreciate their salary offer, but it doesn't address why you're interested in the new opportunity.
If the reason you're leaving is for salary, make sure to point out not only the better salary but also how you got to the point of not getting paid as much as you'd like to. I have plenty of friends who have received job offers for extra money, and received 'competitive' counter-offers from their employer. After accepting however, when raises and bonuses come around they get told 'well we already gave you such a generous pay increase to stay with us, so we aren't giving you a raise this year' or 'your bonus is lower this year because after your raise it's not in our budget to give you a large bonus this year'. So if the company comes back with a big pay increase to try to get you to stay, you have to point out to them that you're leaving because you're unhappy with the promotion/raise/bonus structure at the company, not your current salary rate.
Basically, whatever you tell them, make sure its honest. If you don't like your projects and company politics, and you tell them that you love the company but you're leaving for a higher salary, don't be surprised if the company comes back with more money. Then, when you turn down the counter offer, they'll have sentiments along the lines of "Well what the heck man?? Do you know how many hoops we had to jump through to get you this offer? We thought you really wanted to stay with us. You told us you would stay if we matched your offer and now you're not going to?". If you're genuine and honest with your employer about why you're leaving, a good employer will understand.