Yes and no.
Any paid apps you have purchased through the Market are linked to your primary Google account, so those can be redownloaded without charge.
Also, any of your contacts saved to your Google account can also be synced.
However, anything that has been added locally to the phone that is not synced to your Google account, which includes free Market apps, will not transfer to your new phone.
My recommendation is to make a backup of both your apps and your contacts. For your contacts, simply press menu from the contacts screen and select the import/export option. This will allow you to save your contact info to your SD card, which can then be inserted into your new device and then uploaded.
For apps, there are several different ways. If you set up an appbrain.com account, you can use that to backup the list of your apps for easy reinstallation on your new device. There's also some good free apps on the Market, I personally have used AppManager, which will save your app list to your SD card for easy retrieval later on.
Hope this helps!