That depends. The seller is expected to leave behind all "fixtures"-- that is, all items that are permanently affixed and integral to the house and property. Classic examples of fixtures are ceiling lights, wall-to-wall carpeting, custom window shades and curtain rods (but not necessarily the curtains, depending on local tradition), built-in appliances, and any trees, plants, or shrubs with their roots in the ground as opposed to in pots. (Picture moving into the house and discovering that any of these had been ripped out before the seller left, and you'll get the idea of why they're considered fixtures.)
Within the disclosure or other documents prepared by the sellers, however, they may indicate plans to leave certain items -- and not others. You can always negotiate over these, particularly in a slow market. If you can't imagine the house without the beautiful urns on either side of the front door, ask for them. The seller might throw them in, or at least agree to sell them to you separately.
To learn everything about home-buying from mortgages, agents, inspections and more, see Nolo's Essential Guide to Buying Your First Home, by Ilona Bray, Alayna Schroeder and Marcia Stewart (Nolo).