If your points are in the USA, you can use the free streetmap network dataset that comes on the data and maps dvd. it is ready to use network and have time and distance attributes.
You can also the Find Route tool (next the binoculars) on the standard toolbar in ArcMap. It will use the online service to return you back the routes.
I have had better luck downloading the Tiger center line data set. There are two versions the one that is ready for geocoding and the one that is 500% more complete but takes a lot of work to set up.