I have transited/layed over in SIN several times. Here is some of what I have learned:
Ambassador Transit hotel vs Crowne Plaza: compare the total cost of your layover. Since the Ambassador transit hotels (3 locations, one in each terminal) charge for a block of 6 hours (currently $68 sgd with tax) you are getting a small room and a TV with a few channels for a short stay. If you need 2 blocks of time, you might be more comfortable to spring for the more expensive Crowne Plaza ($160usd/nt approx) which has beautiful, fully equipped rooms and better TV service. Crowne Plaza is accessed via the unsecure side of Terminal 3, so if you decide to go for the Crowne Plaza you will have your bags tagged to SIN, reclaim your luggage, and take it with you to the hotel. If you have packed a change of clothes in your carryon and DO NOT want to reclaim your luggage, see the notes below. Immigration is a breeze for US citizens.
Interlining baggage: not a big deal. SIN is the best airport I have ever seen for this.
If your airline will tag your bags all the way to final destination, you can do so if you choose. Many airlines will not do so, or cannot do so, because their computer system refuses to allow that long of a layover (over 4 hours). If this is the case, and the bags can only be tagged to SIN, it is not a problem. All you have to do is stop at a transit desk inside the airport (secure side) after you disembark from the plane. Show them your e-ticket for your onward flight(s), your luggage claim tags, and they will print your boarding pass and have your bags re-tagged to your onward destinations. No hassle. You do not have to go thru immigration or baggage claim. These instructions are also given in your confirmation email if you book a room at the Ambassador Transit Hotel, since you would not leave the secure side of the airport for this stay.
There is a skytrain that runs from 5am to 2:30am between the terminals. There is a small shuttle bus between terminals from 2:30am to 5am, you will need to ask at the information desks in the airport to locate the exact spot where this bus stops. It is not marked with a sign for some reason.