I only have personal knowledge of Delta and United.
On Delta, you get unlimited domestic privilleges, 18 free transoceanic passes per year, and unlimited service free oceanic passes per year. You also get 18 "buddy passes". Your immediate family (spouse, dependent children) get the same benefits you do. You can also either nominate your parents or a "travel companion" for benefits which include 18 free domestic passes , unlimited domestic service fee passes, and 18 transoceanic service fee passes.
United has a similar system of "Write Your Own" (WYOs) where they issue you a ticket book and you simply write passes for yourself and your family. These are now free. However, it's been a few years, so you may want to check on the details of someone currently there for this one.