How likely is it that AES-256 is crackable within 100 years (2120)?
I want to know if AES-256 will be safe throughout our life time.


No one knows that.  Here is what we do know:


A brute force search (by conventional computers) will be totally impossible.  This can be shown by a power analysis of the minimal amount of power used per step (the minimal amount of power to change a state is $kT$, where $k$ is Boltzman's constant circa $1.38 \cdot 10^{-16} \text{ erg/}^\circ\text{K}$, and $T$ is the temperature in Kelvin.  If we assume a computer that's running at cosmic background radiation temperature ($3.2 ^\circ K$), the minimal energy to step a counter though $2^{256}$ keys would be about $5 \cdot 10^{61}$ ergs; the annual output of the Sun is about $1.21 \cdot 10^{41}$ ergs, so unless you can harness a considerably larger output than our Sun within 100 years, this is impossible
A Grover's search (by a Quantum Computer) will also be impossible.  In theory, Grover's could find a 256 bit key in $O(2^{128})$ steps (which is far more achievable than the $2^{256}$ steps in the previous paragraph), it turns out that, to achieve this "low" amount of computation, Grover's search would require $O(2^{128})$ sequential AES evaluations (where you can't start the next until the previous one has completed).  If we assume that our Quantum Computer can't compute an AES function in less than a femtosecond ($10^{-15}$ seconds [1]), then this would take $10^{16}$ years, rather longer than your 100 year deadline.  To meet your deadline of 100 years, you would need to split up the key space into $2^{94}$ parts, and give each part to one of a total of $2^{94}$ Quantum Computers (each one performing AES operations at this completely unrealistic speed).
Cryptographical advancement (that allows an attacker to recover the plaintext without trying all possible keys); this is an open question.  I personally don't expect a total break; that is, something that, given a reasonable amount of ciphertext (and possibly some known plaintext), will allow them to decrypt; I wouldn't be that shocked if someone in the next hundred years found a theoretical break (e.g. $O(2^{150})$ effort given vast mounds of chosen plaintext).  However, this is what people are worried about (as it is easy to see that the other two break methods are totally infeasible).




[1]: For reference, a femtosecond is approximately the time it takes light to travel 0.3 microns; this implies that our AES evaluation engine must be considerably smaller than your average bacteria...