Modern cryptographic systems are essentially unbreakable, particularly if an adversary is restricted to intercepts. We have argued for, designed, and built systems with 128 bits of security precisely because they are essentially unbreakable. It is very easy to underestimate the power of exponentials. 2^128 is a very big number. Burt Kaliski first came up with this characterization, and if he had a nickel for every time I tell it, he could buy a latte or three.The whole post is good and goes on from there to talk about real and possible vulnerabilities in cryptosystems (for example, the government could break into your house and put a keylogger in your computer for a fraction of the cost of attempting to break the crypto). Link
Imagine a computer that is the size of a grain of sand that can test keys against some encrypted data. Also imagine that it can test a key in the amount of time it takes light to cross it. Then consider a cluster of these computers, so many that if you covered the earth with them, they would cover the whole planet to the height of 1 meter. The cluster of computers would crack a 128-bit key on average in 1,000 years.
If you want to brute-force a key, it literally takes a planet-ful of computers. And of course, there are always 256-bit keys, if you worry about the possibility that government has a spare planet that they want to devote to key-cracking.