Though the alcohol burns off during cooking, if you still prefer not to use it, in most cases you can use pure fruit juice. Apple, grape, etc. I wouldn't recomment using sweetened juices, unless that's the taste you're looking for. You can also mix in flavoured vinegars, but the balance between the juice and vinegar is tricky.
None of the above is quite as good as alcohol, but...
Trilliumpath is right, the alcohol will evaporate in cooking, however, your "sub" for alcohol depends a great deal on the alcohol in the recipe. For example: *Amaretto(Almond flavored liquor)-you could sub in almond extract *Rum-you could sub pineapple juice mixed with almond extract or molasses depending if it is light or dark rum. There is also rum extract. *Red wine-beef stock or red wine vinegar diluted with grape juice. Also, keep in mind there are quite a few non-alcholic versions in the liquor isle so do consider those with list in hand when shopping.