The three common contingencies are 1) the buyer obtains the necessary financing,  2) the home appraises at or above the agreed upon price, and 3) the buyer and seller resolve any issues, if any, raised by a professional home inspection. There are usually time limits in the purchase contract for each of those contingencies to be satisfied or removed.  There may also be other contingencies ("Seller to remove three junk cars from front lawn", or "Buyer to provide additional deposit of $X,XXX by YY date".)  Almost any contingency can be written into a sale agreement, so long as buyer and seller agree.  

 

I recently wrote an offer for a buyer which included the contingency that the appliances were included, as they commonly are.  The seller was planning on taking them out when they moved, so the seller did not accept that contingency (and therefore wrote a counter offer specifying that the appliances were not included)