My uncle brought up this question yesterday. His position was that it really made little sense for Germany to align with Japan given the distance separating the countries. He went on to suggest that if the US doesn't get involved, England very well may have fallen, causing the US to lose their main staging area for troops and supplies, most likely causing the US to utilize Africa. Also the US doesn't attack Normandy in that situation. The US also likely wouldn't have supplied arms to Russia, due to the neutrality pact signed between Japan and the Russians in 1941. So my question is why Germany would declare war on the US? Did the Germans just do it because of their ties to the Japanese?
Basically, Germany didn't want the US to get involved in the European theater anymore than they already were and thought that allying with Japan would be enough of a deterrent to the US while also helping to cripple Great Britain by cutting her off from her territories in the Pacific. The US had also cut Japan off from the resources they needed by way of trade, so by allying with Germany, they felt free to continue their march throughout the Pacific (including into British and French territories).
The Tripartite Pact signed by Germany, Italy, and Japan didn't necessarily require that Germany and Italy declare war on the US after the Japanese attack, but they did (partially because they thought Japan would attack the USSR and draw some attention away from the West) because of their alliance.
Check out John Keegan's book The Second World War if you have the time. It's pretty thorough.