Alright. I left off saying that there was a more spiritual connection to this. However, be warned: It's nothing nice.
Firstly, there is the concept of a soul. The image we have burned into our minds usually involves pearly white humanoid shapes that phase in and out of perception. Many people believe that one's consciousness originates from their soul. The soul, apparently, is a metaphysical force that contains each and every shred that make up our personalities. The soul is our conscience, our source of free will. Or at least, that's what they like to think.
Neurology says otherwise. Everything that the soul does, is the work of the brain. Memories? Cerebrum. Emotions? Chemical messengers. Conscience? Also the cerebrum. All self-awareness is simply generated by the brain. As Suresh says, if the soul exists, it exists in the brain.
But you argue, if the soul isn't really something... that is... you, then why do we all feel that we are unique? Why, aren't we like other animals, living apparently with little to no conscious thought? I'll answer the second one first. The reason is simple: Our brains are simply much more developed than theirs'. Notice how higher-order primates also appear to have reasonable cognitive function? Orang-Utans, with their frighteningly human resemblance, are widely known to have sapien function. They can learn how to get around a problem in more than one way, as well as come up with new strategies to approach a task. Those actually mean the same thing, but I know most of you wouldn't have noticed. Note: Do not write like this for school papers. The trend can be easily seen as we progress from primates to rodents, reptiles, and amoebas. The more developed the brain is, the more conscious thought an organism can have. Many people have this perception that dolphins and whales have souls, too. But notice how their cerebrums are almost as highly developed as our own? Coincidence, no?
Alright, fine, so we know we have highly developed brains, and so we have much more conscious thought. What about a sense of identity? Well, you're not going to like this. Say your name, over and over and over again. Yeah I'll let you do that for a few minutes. After a while, you'll find that your name is just a bunch of random syllables that were put together. As your name loses meaning, so does your identity. Now, let's take a step further and find a mirror. Now, stare, I really mean, stare into the mirror for a while. As long as it takes. Suddenly, you'll realise that it's just another face. Another human being, one of the 6.5 billion that inhabit this planet. Your "self" is not special. You are not special. The only way you are unique is that your genetic code is not identical to anyone else's('lest you're from a set of twins/triplets/whateverets).
If that doesn't reduce the notion of a soul to dust for you, I'm either not arguing my point properly(which is likely), or that you're really strong willed(which, is also likely).
Many people(three times this post!) claim that proof of the soul lies in those out of body experiences. Conveniently, they happen during events like prayer, or séances. There's always a spiritual connotation with an out-of-body experience. However, there are several very mundane reasons for this. One, and most importantly, it's just an illusion. During an out-of-body experience, your brain is tricked into thinking that it's receiving input from a place outside of your body. It's comparable to an amputee having an itch in his severed leg. It's not really happening, but your brain is confused and wired wrongly. Two, the conditions that cause this to happen are easily reconstructible. Reduce your oxygen intake and your brain does funny things. Increase your oxygen intake and your brain also does funny things. Sitting for hours during a prayer session can cause that to happen. Also, with a bunch of electrodes and some magnets, anyone can have an out-of-body experience. It's been done countless times in hospitals and laboratories. In fact, I'm thinking of setting up a kind of business... to commercialise the what must be an awesome feeling... yes...
Okay, I've gone on a bit. You must be wondering what all this has to do with cloning. You see, science has tried to disprove the existence of souls for decades. I mean, metaphysical=pure bovine excrement to a scientist. That's just a long way of saying "bullcrap", if you didn't catch it. Go google "bovine". Learn something new every day! Anyway, back to this...
Here's the logic: Soul believers say that conscience and emotions all stem from the soul. This also means that a soulless being would have neither the ability of conscious thought, nor be able to experience emotions. This is where cloning comes in. When you clone someone, you clone his body, and his body only. No soul. There is no clingy spiritual force that resides within the clone. So, we do a small exam. Can the clone laugh, cry or get angry? Can he solve a Su-doku puzzle, or learn to ride a bike? If he can... then there we go: Souls do not exist. If a soul exists, it doesn't have any of the uses that people think right now.
Of course, we can expect a similar breed of people to the Creationists who will try to come up with some...lame... counter-arguments. Like that souls can be born out of nothing. Oh yeah, and G_d did it, as usual...
If I ever shared this point of view with my family... Well I don't want to think what would happen. They've always been open about my choices, but I think this one just goes too far for them.
Yes, you waited that long just for this. I know, there are probably some loopholes in my hypothesis, but if someone can point them out, I'll gladly try to fix it, and admit defeat if I can't. Unlike the opposition, who uses the age-old reason of you-know-what. Spitting in the face of logic, again.
Yeah... and as a follow-up from that picture a few days ago...

Don't worry, it's not my hamster. My hamster died when I was thirteen.
-Joe