Lilacs are usually pretty reliable bloomers, but sometimes they fail to bloom. For some, they always seem to fail (we'll get to that).
Commonly, insufficient light is the culprit in lilacs not blooming. They may have been planted at a time when trees weren't as mature as they are now. They probably flowered great at first, but now that the trees around them are larger and provide more shade, they haven't been blooming so great.
You can either transplant the lilac to a sunnier location, or try and trim the tree to provide more light to that particular area.
Many people have lilacs planted either in the lawn or very near to one. Lilacs prefer a more balanced fertilizer to help maintain beautiful blooms. Lawns on the other hand require high nitrogen fertilizers. The problem is when the lilac is given a high nitrogen fertilizer. It encourages a lot of green growth and great leaves but at the sacrifice of flowers.
Be sure to provide your lilac with a balanced fertilizer and avoid using high nitrogen fertilizers around it.
This is easily the #1 mistake that most people make. Lilacs are what we call "old wood bloomers". That means that they set their flower buds on old wood, or the past season's growth. Flower buds are also typically found at the ends of branches. If you were to go out and prune your Lilac in late summer or fall, you just cut off your flowers for next year. The same goes for early spring (before they bloom at least).
Make sure that you prune your Lilacs (and all old wood bloomers for that matter) shortly after they are done flowering. That means that when we get to the end of May and your Lilacs don't have any flowers left on them, it's time to prune if needed.