The security of your randomly generated 15 characters password depends very much on how it is stored on the system that is being breached.
If the system stored it in clear text, your password would be stolen in 0s.
Assuming the next worse case scenario of your password being stored as an MD5 character that is being hashed just once, without salt, if there exist a super rainbow table (beyond yottabyte size?) with search space depth of
95^15 (you forgot to include space), your password would be cracked in a matter of hours or minutes.
Without a rainbow table, the attacker would have to brute-force your password by guessing one at a time. Jeff Atwood had written an article on hashing speed which I quote here:
MD5 23070.7 M/s
SHA-1 7973.8 M/s
SHA-256 3110.2 M/s
SHA-512 267.1 M/s
This was what an expensive GPU can achieve two years ago. If Moore's law continue to predict correctly for the next 100 years, then the hashing speed for MD5 with a GPU, if GPU is still the tool for cracking hashes, will be:
Year MD5 hashing (M/s)
2014 23070 x 2
2016 23070 x 2 x 2
2114 23070 x 2^51 = 5.2 x 10^19
Your search space of
95^15 will yield
4.6 x 10^29 possible hashes. Let's assume the hacker tries every single one of them in 2114, the number of guesses he can make is:
5.2 x 10^25 x 365.25 days x 24 hours x 3600 seconds = 1.6 x 10^33
Which is more than
4.6 x 10^29. Therefore it is possible to crack your password in MD5 before the end of 2114.
The next consideration is how much computing resources does your attacker has? If one GPU is not enough, can he get 10 or even 10,000 of those?
Finally, password cracking is not cost-free. GPU consumes energy. Your attacker got to think, is it worth it? To run those machines for years just to brute-force a password when they could have just hire someone to beat the crap out of you to get it at a fraction of the cost and time is plain stupidity.
In summary, your randomly generated 15 characters password is good for the decade, but hard to say for the century, provided that the system storing the password is using a MD5 hash or stronger and that you have not accidentally revealed the password yourself.