As your body no longer posesses muscle control, initially your muscles relax (prior to rigor of course). This has the unfortunate consequence that your body releases various contents that it was holding in. This is rather unpleasant for those who have to deal with your corpse. In addition, my experience is that some of your stomach contents (acids and the like) and saliva tend to come up through your mouth and nose. This is also rather unpleasant for those who have to deal with your corpse, particularly if they are perfomring CPR on you (maybe because you are only mostly-dead?). The chest compressions and bag-valve mask can expell that stuff. Now the above is pretty much the immediate consequences. If you wait just a little bit longer, due to a lack of circulation and the effects of gravity, all your blood pools at the point closest to the ground. So if you are lying on your back and someone was to turn you over, your entire back would look bruised. This is a sign that yes indeed, you are quite dead. Rigor should be setting in soon as well. If you are lucky, you have loved ones who are quite distraught at your passing. If that is not the case, the orderlies in the institution you live in may simply be upset with the mess they have to clean up. Of course we could go further in depth as to what happens over time with decomposition and the like, but my impression is you were more interested in the immediate consequences of death. Now keep in mind, the exact answer to your question "what happens when we die?" really could vary depending on how the unfortunate event occured. For example, one of the consequences of a fatal heart attach rarely includes your brain matter being splattered across your windshield, but other methods of death might very well include that step. Hope I've helped.
I saw on Discovery that the coroner can tell how long a body has been dead by examining the type of insects that are feeding on the corpse. Apparently certain insects only show up after other insects have had a chance to pre-digest you. In essence we are all just food for the insects.