Interestingly enough, we just returned from picking out a new item that was a replacement under warranty.
Four and a half years ago we purchased a DLP HD TV. It was the floor model so we chose to spend the extra $400 for the extended warranty. A few months later, the original light bulb burned out so they replaced it under warranty. Now, within a year of getting the TV we noticed a loud buzzing noise, but thought it was just the fan. We found out about 4 months ago that it is a particular part that was causing the problem and it was a common defect. I called for service and the tech came out, confirmed the defective part, and ordered it. Saturday, after waiting more than 3 months for the part to come in, I had finally had enough so I called the warranty company and basically said that 3 months was long enough to wait, and they either needed to confirm that the part would be available shortly or bring us a new TV. I was pleasant, but I wasn't backing down. Long story short they called yesterday and said that the replacement had been approved. They were replacing the TV with a 52" Sony Bravia LCD, or we could chose another TV that was the same price or lower than that model. We chose to go with a smaller size (52" is too big for the room it is now anyway) but upgraded the model to two models higher in quality than the one we were offered. We chose a 46" Sony Bravia something something VE. It has a higher resolution and a few more features than the larger model. The best part was it was actually $200 more than the one we were offered, but on sale for the same price! We paid a whopping $10.70 for some government fee to recycle the old one (which we get to keep, by the way, so it will go in the basement for the kids to play video games on...all of a sudden that buzzing sound isn't so annoying!)
So, I guess the short answer to your question OP is, it depends. It depends on the warranty that came with the item you purchased. Our warranty said if it couldn't be repaired it would be replaced with a new one. They no longer make the type of TV we have, so we lucked out with a new LCD. If your warranty said you get a new item, then it should be new. If it says they can replace it with a refurbished item then you may be out of luck.
T