Over the years, there have been substantial periods of time when cryptographers have out-done cryptanalysists, and vice versa. For the Internet to work, there must be security, and so the cryptography must be able to withstand all cryptanalysis techniques. Pretty Good Privacy provides this, since it gives security that is safe for people to use.
Pretty Good Privacy relies on one symmetric and one asymmetric cypher, usually IDEA or 3DES, and RSA. Together, with RSA encrypting the keys and IDEA or 3DES encrypting the rest of the message, this is impregnable without a huge computing resource, which no one has been able to build. Computing power tends to increase year after year, but so does work on prime numbers, and so for now, RSA will be able to keep increasing the length of its keys as fast as computers can speed up their factorisation. This should keep RSA safe for many years.
Cryptography has developed so fast recently, and its implementation is expanding so fast across the Internet, that governments are having to think quite fast about the implications, including the possibility of terrorist organisations using cryptography to aid their cause and avoid the law. For the time being, the success of e-commerce and the public feeling in favour of privacy for everyone is likely to stop legislation being brought against strong cryptography. A major terrorist disaster that could have been prevented had the criminals had no access to cryptography could change the public opinion, and force the government into action; this would have grave effects on Internet trade, and hopefully it will not happen.
At the moment, one of the other threats to security is that of human error, such as poor implementation, and until either quantum technology takes off, or new mathematical advances develop a fast factorisation method, this is likely to remain the limiting factor.
However, this is not a particularly severe problem, and so at present cryptographers are winning the battle over cryptanalysists, and I expect this will remain the case for many years to come, if the law allows them to.