Or it may happen rarely. Maybe after an almost infinite time. But what happened once can happen again when there is an infinite amount of time available.

That is the entire point of living the same life forever on repeat.  If time is infinite then it can happen again and it will happen again, you are forever going to relive your life.

Heh, the nihilistic perspective of this is fun to think about.  Would it be more depressing to live in a universe where everything you do doesn't matter because it is doomed to repeat endlessly exactly the same, or to live in a universe where everything you do doesn't matter because it is doomed to heat death?

Life and the universe do not matter.
For life and the universe is condemned to die.
Whether the universe dies a heat death or not.
An endlessly repeated cycle is not possible in my opinion.
I think every universe must have some 'loss'.
So there is less and less 'universe'!

that there are many versions of you, living all possible lives?

I do not believe in the meaning of the universe and I do not believe in the meaning of life in general.

But I believe in the meaning of life in particular.
I believe in the meaning of my life. That I can ask myself whether the universe has a meaning, and how the universe works, is the meaning of my life. Amongst other things.

I do not believe in a cyclic universe in which the same play is played over and over again. This would contradict quantum theory, in my view.
But I believe that cyclic universes are possible in the sense that they expand, contract, expand, and so on.
But if we live in such a universe, ours may be the last one in the series. For obviously the matter in our universe is not enough for it to contract again.
The amount of energy and matter in these universes may always be the same, but the distribution may always be different.
The initial distribution of matter and anti-matter may be different. Perhaps there was a universe before us that contained more anti-matter than matter, so it was an anti-matter universe.
And in our universe now, the difference between matter and anti-matter is so small that only so little matter is left that it no longer suffices for a contraction of the universe.

Actually, however, I believe that universes are created and disappear like blossoms that bloom and wither again.
This may happen now. Somewhere outside our universe, perhaps, a new universe is being created right now. Or many universes.
Or it may happen rarely. Maybe after an almost infinite time. But what happened once can happen again when there is an infinite amount of time available.

But first, there are a lot of other lives to live. All imaginable lives!

I don't think that applies because you are a result of what has happened to you and what makes you up.  This sorta notion suggests you can only be you in the life you are living now so everything else is not you.

that there are many versions of you, living all possible lives?

Well then they aren't me since I am not them.  For you to be who you are now you must have had the previous experiences and stored memories of those experiences and be the combination of all the physical processes going on inside you right now.  Without those fairly specific things then you are not you.

It's the reason why if we have a twin, our twin is not the same as us.  We are the sum of both our genes and our experiences

and I would make another decision, another event would happen: I think I would still be myself .

And you are you now.  Who you are is dependent on the state of your brain, the progression of self is an illusion of those processes. 
To put simply, you can't be someone who isn't you because you are you. 
This is a similar notion to the anthropic principle, you can't be somewhere you can't be.

It's the reason why if we have a twin, our twin is not the same as us.  We are the sum of both our genes and our experiences

Brain and/or head transplant.

There is a parallel to be drawn between the cyclic universe and the cyclic life.  I also believe in the cyclic universe but things do not repeat in the same way, therefore it is a new universe.

Possibly, if we can ever do that.

A more efficient means would be if we can transfer our brain's electrical signals into a metal body and thus retain our sense of self in a body that can exist indefinitely- do you think this will ever be possible?

And do you think that mental telepathy will ever be possible at a higher level of evolution?

There is a parallel to be drawn between the cyclic universe and the cyclic life.  I also believe in the cyclic universe but things do not repeat in the same way, therefore it is a new universe.

Could be a reset, not a recollapse but a reset, same conditions leading to same conditions on repeat.  Universe expands to a point where it is at maximum entropy, reaches almost exactly absolute zero, macro scale quantum events, tunneling of particles, universe restarts.  A closed system of eternally expanding dead shells of spacetime where they inevitably lead to a rebooting process.  This would be you reliving your life over and over.

Possibly, if we can ever do that.

[youtube]_EHCHv5u3O4[/youtube]

A more efficient means would be if we can transfer our brain's electrical signals into a metal body and thus retain our sense of self in a body that can exist indefinitely- do you think this will ever be possible?

Maybe

And do you think that mental telepathy will ever be possible at a higher level of evolution?

No.  Sending text messages between brains should be possible though

 I will post soon my mod page again !