Do you ever feel totally brain-dead when listening to a sermon or reading your Bible, like it has no effect on you?
John Piper suggests praying Psalm 119:7. Open my eyes that I may see wonderful things in your law.
Another thing I can suggest is to try another language! I was totally tuning out during a sermon recently and I was realizing that it's because it was in English, and English sometimes sounds like "blahblahblah" to me. In your native language, you can skim books and still get the gist, and also tune out parts of conversations and still know what's being said (not that I would ever do that!).
So when I go to read the Bible sometimes...I know who's going to win and who's going to lose, and I'm not always interested in the journey to get there.
In Russia, I have to pay close attention to sermons and readings, simply because if I miss a few words, I risk missing the point. In another language, it makes a big difference if you miss key words like "not" or "but" or fail to identify the verb tense.
Pretty soon I will probably start tuning out Russian too and will have to find a new language!
Another idea is to simply read a different translation, but that can sometimes be distracting because you might focus too much on the words that are different stylistically but not tied to the main point. Still, I think variation is good.