My main reservations with this fall under the 'Bones argument'.
Transferring the brain seems possible, although due to cellular deterioration the brain will eventually fail (copy of a copy of a copy etc. of cells...). Brain Cancer won't be going away, and there are other disorders as well. So I don't see a brain holding up for hundreds of years, let alone thousands.
Transfer of consciousness I'm not buying. I can see a machine that perfectly copies your neuron patterns, etc. into an artificial brain, but it will be exactly that, a copy of a person's memories, not that person's memories. Your copy will live on, but you still die when your brain does. So your 'clones' may achieve relative immortality, but you still die.
A way around this would be some sort of artificial cell replacement of the brain that happens gradually (i.e. replace a 'less reliable brain cell with longer lasting/more robust cells, perhaps through DNA manipulation), so that your brain impulses remain 'homogenous' during the process instead of being copied, and indeed our bodies replace cells fairly regularly, but I don't see a 'transfer' being possible. At least not in the next century or two. Copy yes, but does the copy have a soul, etc.?
Then there is the whole Skynet scenario thingie...