Very much so, and while oil is the most obvious resource we depend on, we also get large amounts of other resources like selenium, aluminum, gold and molybdenum from other countries. These are essential to manufacturing sectors of the economy, especially the high tech and military weapons industries. If all imports of these ended tomorrow, our economy would also suffer greatly, and the US goes to great lengths to secure them.
I guess this depends on what you mean by "rely." We certainly have resources of our own, but our economy would be in grave trouble if that were all that we had.
The most obvious resource that we have to get from other countries is oil. Of course, we have some of our own oil (some of which is spilling into the Gulf of Mexico as we speak). But our own oil is not really enough to satisfy all our needs and we have to import a lot of oil.
We could survive as a country without foreign resources, but we would be a lot poorer.
Yes we do,