Buddhist meditation is not about emptying the mind. At its most basic level, it's about taming the "monkey mind" that rules our lives - the inner cacophony of disjointed worries, fears and pointless chatter that dominates most peoples' days, to the point that they are completely out of touch with the present moment. If most people could read a 500-page second-by-second description of the disjointed thoughts that have passed through their minds over the past week, they would wonder why they hadn't been committed to an asylum. Try paying attention to all the places your mind wanders over the course of a mere 30 minutes, and how little any of them have to do with the reality of the present moment; it's quite a sobering exercise. The objective of basic-level Buddhist meditation is to reduce this out-of-control inner chatter and achieve a level of mindfulness that will carry over to daily life. The initial focus is usually on the breath; when the mind wanders or becomes distracted, the individual does not fight it but merely brings the focus back to the breath. (I'm obviously not promoting Buddhist meditation since it is inseparable from the religion; my point is just that the technique is basically the same across all religions.)
The book of Eastern Orthodox theology that I happen to be reading likewise emphasizes that a blank mind is not a tool or goal of meditation. The Orthodox focus on the Jesus Prayer: "Lord Jesus Christ, Son of God, have mercy on me, a sinner" - first for basically the same reason the Buddhists focus on the breath (to silence the inner cacophony), then gradually to internalize the profound meaning.
I don't think many people, including me, are really good candidates for formal meditation in the sense of, "Now I am going to sit and meditate for 20 minutes." However, I often reach a meditative state on long walks or long runs. By this I mean a state where the inner cacophony is silenced and the Holy Spirit can be heard more clearly. This state can be achieved by meditating on specific Bible verses, but more often I'm just trying to maintain the prayerful attitude of thanksgiving described in 1 Thessalonians 5:16-18 (NASB): "Rejoice always; pray without ceasing; in everything give thanks; for this is God’s will for you in Christ Jesus."
Edit: I forgot to say that the classic of Christian contemplation/meditation is The Cloud of Unknowing, written by an unknown mystic in the 14th Century. In a good modern translation, it is very easy to read - and the technique he describes is basically identical to Buddhist meditation, but obviously in a Christian context.