This is a really interesting thread, maybe it's bad of me to "bump" it, but if I can, I would like to post my thoughts as contribution to the conversation.
Everyone has made valid points, and I would like to reply to some of those points.
One member raised the question: What makes Romanov reincarnate claimants feel their lives are superior to that of the Romanovs? (i.e. They were explaining the reincarnation belief that as one's soul travels through different bodies, the lives become increasingly better.)
It's a really good point, but I would wager (perhaps some claimants DO think they're better than the IF, I don't know), but I would think that most claimants believe in this life they aren't "better" per se than the Romanovs, but that their conditions have improved. If I look at my own life- No, I'm not wealthy or powerful, my family does not own the biggest empire, etc. But I think that my life is probably more enjoyable than the Romanovs' was, for the simple facts of:
a) I am not in the public eye, I do not have to worry about the judgement of millions
b) I do not have an ailing brother, on whose shoulders the fate of my country rests
c) I can marry who I wish to marry, regardless of their "class"
d) I am not confined in the walls of my home
e) There is no rebellious group trying to murder my family
d) And of course, I have yet to be dragged into a cellar room and executed.
So, I would say my simple life as a university student in Finland, spending time with my friends, family, and the one I love, without any of the aforementioned worries, is more enjoyable, and free. Yes, the Romanovs had pleasant times, but they were short, and often shadowed by Alexei's illness, the state of the country, etc. etc.
Another good point was concerning the legitimacy of claimants. Too often, (and I agree) people claim they are someone of importance simply to make themselves feel important. Maybe they aren't comfortable in their own shoes. But I would like to make the case for true reincarnates; These are people who recognize who they WERE as being a separate person than who they now ARE. If I were to believe I was Anastasia or some Titanic passenger, (what-have-you) I'd like to think I could separate the past from reality. True reincarnates, I believe, do. Just because Anastasia drank Coke (example) doesn't mean a true Anastasia reincarnate drinks Coke. NOW you may prefer Pepsi. Anastasia liked to take photos. Maybe you despise cameras. That doesn't discredit one's legitimacy, and on the other side of the coin, just because you like Coke and taking photos doesn't mean you are a reincarnated Grand Duchess.
As others have said before, it isn't necessarily similarities between the claimant and the person they are claiming to be, but rather the memories, the ones only that person holds, without ever reading it in some research; thus it makes any claimant hard to prove.
I don't as a general rule believe in reincarnation; but there are individuals I do believe. As an Orthodox Christian it's difficult to mesh these beliefs, so I have to be careful who I trust. But I hope I keep more of an open mind than some here who have said, "All claimants are idiots" or whatnot.
~RomanovMartyrs