Only once did someone tell me I should in the 3ish years I've owned my Kindle. I thanked him and then ignored the suggestion and still have never had to actually take it out. No problems at all leaving it in the bag.
I usually take my iPad out, but I forgot to take to take it out of my rollaboard when I went through security at MIA this weekend. I was too busy focusing on how I was going to berate the TSA agent doing my upcoming patdown. Funny they didn't say anything about my iPad being in my bag (or my liquids) but notice the 1.5" SOG keychain knife that has gone through every airport checkpoint for the past 2 years, and confiscated it.
Seems that it all depends on the TSO. I had an issue with one this last weekend because my iPad, SLR, extra lens, and binoculars were all in one bag - he said the bag was "too dense" and totally unpacked my bag into two bins to re-run through the x-ray. He let me know several times that in his opinion iPads should always be removed from the bag because they had a "huge power supply."
He didn't think it was funny when I told him I suspected he just wanted to see if I could repack my bag..... Humorless sort, he was.
Only one other time have I had anyone make me take the iPad out of the carryon bag.
i have an ipad and its gone either way, there are times i leave it in and it goes through, and theres times they pull it out and say it must go through separate, really depends on how lazy the TSA agent is.