This is a question that agents get asked more often than not. In order to best answer this question, let's take a look at the One to Four Residential Contract for the state of Texas.
Section 2 of the contract covers property, improvements, accessories, exclusions, and reservations.
2B- IMPROVEMENTS: The house, garage and all other fixtures and improvements attached to the above-described real property, including without limitation, the following permanently installed and built in items, if any: all equipment and appliances, valances, screens, shutters, awnings, wall to wall carpeting, mirrors, ceiling fans, attic fans, mail boxes, television antennas, mounts and brackets for televisions and speakers, heating and air-conditioning units, security and fire detection equipment, wiring, plumbing and lighting fixtures, chandeliers, water softener system, kitchen equipment, garage door openers, cleaning equipment, shrubbery, landscaping, outdoor kitchen equipment, and all other property owned by the Seller and attached to the above described real property.
2C-ACCESSORIES: The following described related accessories, if any: window air conditioning units, stove, fireplace screens, curtains and rods, window shades, draperies and rods, door keys, mailbox keys, above ground pool, swimming pool equipment and maintenance accessories, artificial fireplace logs, and controls for (i) garage doors, (ii) entry gates, and (iii) other improvement and accessories.
2D-EXCLUSIONS: The following improvements and accessories will be retained by Seller and must be removed prior to delivery of possession: _________________________
After looking this over, you have to take into consideration the phrase: Permanently installed and built in items. Things like washers, dryers, and refridgerators are not permanently built in. These items are almost always removed by the Seller. When making an offer on a home, you can always ask the seller to leave these items, or ask if they will sell them to you.
Most agents use the this rule of thumb: If there is a built in / designated space for items, those items should stay. However, if you can unplug them and move them, the Seller could technically take them.
I always ask my sellers if there are any permanently installed items they wish to keep. Sometimes they have great grandma's mirror in the bathroom, or Aunt June gave them the chandelier in the hallway. Those items must be in the exclusions list and must be replaced before closing. You can not simply just take them down and leave nothing there. My advice on these things is to remove them before you even list your home for sale. That removes all doubt when it comes to those items.
Now, keep in mind, I am not an attorney and can not give you legal advice on any of these items. If you have questions, you will need to contact an attorney of your choice for clarification.