For sellers, multiple offers are great. Competition will drive the terms and conditions of the sale to the most desirable levels for you. For buyers, ehh....not so great. This means that you are in a bidding war and you might have to go a bit out of your comfort zone, if you truly want the property.
Typically when multiple offers come in on a property, the sellers and listing agent will alert each party of this and set a deadline for each potential buyer to submit their highest and best offer. Let's take a look exactly what "highest and best" means. First off, notice it does not just say highest. Often times the highest offer truly is the best offer, not not always.
Say you have 2 offers come in over the weekend. Your home is listed at $129,900. Offer A is for $127,900 with a 45 day close, 7 days to perform a general home inspection and the sellers pays 3% of the purchase price towards the buyer closing costs. Offer B is for $122,900 with a 30 day close and they are waiving an inspection. Right off the bat, you have to remove $3,837 from the top of offer A's purchase price to cover the closing costs. So the offer really is $124,063. I always recommend buyers have home inspections because if there is something wrong with the home, you can back away or ask for further seller concessions. Obviously sellers would rather not have any further concessions, so now offer B becomes quite attractive. With a difference of less then $1,200 at this point and with offer B having no possibility of further concessions, A is not looking so good anymore.
If you are a buyer looking at bank owned properties for investments, cash and a quick close are usually king. If you know that there are multiple offers on a bank owned property, there are few things to help your offer stand out. First; a quick close. The banks want to get rid of these properties as quickly as possible. So cash will help here, if you have it readily available. Second; increase your earnest money. Your earnest money is your guarantee to the individual selling the home that you are intent on purchasing. Increasing your earnest money will help your offer stick out. A reasonable cash offer, with a quick closing time and a higher earnest money deposit, will often do the trick. Sometimes though, you may still just be outbid. Unfortunately, not everyone is allowed to win.