Yep, oil permeates our lives. Or rather the molecules of carbon and hydrogen. If there is an alternative, it would be probably be hydrogen based and one central issue would be solving the storage conundrum. Hydrogen is such a small molecule that it can easily escape - for example if you imagine it in a wine glass with a glass lid on, it will still escape.
Having said that, as others have said, there would still be the need for hydrocarbon chemicals in all their various forms, from gases to ethylenes, compounds like ethanol, acetic acids and their derivatives and all the joyous complexities of organic chemistry - as well as lubricants and bitumens.
The other point is that there is loads of crude still out there - this argument that we are running out in twenty years has been around since I started in the energy business - not only are vast new fields being discovered (wit Brazil, which is becoming the new Saudi) but also within existing fields. Schlumberger are developing down-well microwave extraction - shaking the crude molecules to pop out of their little sponge cell homes. Now take your average field, no more than 30 to 32 per cent can be currently extracted by conventional techniques (primary, secondary or tertiary recovery). Imagine if we can go to 35 to 40% - that's an awful lot of incremental hydrocarbon from existing fields, starting with the large ones first.