Crossover cables are needed to connect computers directly together, also hub-hub, switch-switch, etc. Non-crossover cables (straight through) are needed to connect computers to hubs/switches/routers.
Here's a good reference to the wiring scheme, I'd use EIA/TIA T468B rather than A. No reason, it's just current practice.
http://www.bluemax.net/techtips/netw...estandards.htm