Meditation is one of those words with multiple meanings, and some Christians are frightened by the concept because they think that meditating involves emptying their minds completely and allowing outside spiritual forces to fill the vacuum.
Two people are involved when we meditate — ourselves, and God. Queen Anne’s Lace, original oil painting by Steve Henderson, sold; licensed open edition prints at Great Big Canvas, iCanvasART, and Framed Canvas Art.
(Interestingly, this is a good description of what happens when we sit in front of the TV, chips in hand, but for some reason we keep doing it.)
Emptying one’s mind, however, is not the only option (and indeed, not a valid one for Christians), and meditation upon Scripture involves actively using that mind as we contemplate, muse, ponder, and deliberate over what we are reading.
Please follow the link to Improving Your Meditation Skills at my BeliefNet blog, Commonsense Christianity. You may, or may not, like my suggestions (feel free, always, to comment! I answer to the best of my ability), but it can’t hurt for any of us to increase our ability to read, understand, and grapple with Scripture. (Because if we don’t, there are far too many well paid propaganda artists out there quite willing to do it for us.)
This Woman Writes by Carolyn Henderson 
Again offering a non-Christian perspective. I’ve been meditating for years as part of my therapy for clinical depression and anxiety. I’ve never understood why people “fear” meditation. Perhaps it’s because they are afraid to be alone with themselves. Maybe the evil they fear is their own self-doubt and negative thought.
Having been raised Catholic, I am familiar with the mystics and such from history. Meditation is merely a form of focus. Hildegard von Bingen knew that. The Sufi dervishes know that as they spin madly onward. There are several different forms of meditation, and most of us do it without even realizing it (an athlete in The Zone is meditating as sure as if he or she were sitting in a lotus position chanting “ohm”).
“To meditate upon something” means to give it your undivided attention, which is just what Christians are supposed to with their faith, right? Meditation is a form of prayer in some ways, a gift we give to ourselves that allows us the time and space to connect with something higher. I never feel “empty” when I’m meditating in true form–I feel enormous, connected, whole. Whether this comes from true communion with deity or simply from freeing myself of the distractions that make life small and narrow, I do not dare to speculate. But I doubt anything evil could crash into the space I inhabit when I am meditating. There’s just not enough room for that sort of thing when I’m connected.
Deb — I like your insight, and your approach from a non-religious (because true Christianity is actually much different from what it is portrayed to be in the mainstream) standpoint. Many Christians fear meditation because of its multi-faceted approaches, and indeed, the concept of emptying oneself to be filled with . . . what? is a good one for truth seekers to avoid. God wants us to love Him with our minds, and there is no encouragement that we let go of them. Indeed, meditating upon and with God frequently involves a mental wrestling — I always think of Jacob wrestling with the angels — and very much requires being mentally sharp.
I agree with you that meditation is a form of prayer with a Higher Being. The crucial aspect is to be familiar with who the higher being is that we are inviting to speak to our soul. As a Christian, I ascribe to the knowledge that there are spiritual forces operating around us, and not all of them are benevolent. I encourage you, in your meditation — if it involves invoking the attention of a higher, spiritual being, to reflect on who that being could be, before you get too involved with him/her.
This is a practical matter, actually, and in dealing with spiritual beings, we apply the same sort of judgment and discernment that we do in interacting with flesh and blood humans: who am I talking to? What are their credentials? Are they friendly to me, or not?
Meditating, in the sense of deeply thinking — about anything, actually — is something more people could take advantage of, and I wish they would. If people spent time, like you are, like I am, like people who seek truth are, meditating upon truth, as opposed to playing games on Facebook, we would at least see a growth in intellectual ability and mental acuteness, and the masses — what Big Media and Big Government and Big Business think of the bulk of humanity — wouldn’t be fooled so much by lies.