Yesterday Google announced that it was updating its certificates to use 2048 bit public key encryption, replacing the previous 1024 bit RSA keys.
I have always found the short keys used by websites somewhat shocking. I recall back in the early 1990's discussion about whether 1024 bits was good enough for PGP keys. Personally, I liked to go to 4096 bits although it was not really officially supported.
The fact that, 20 years later, only a fraction of websites have moved up to 2048 bits is incredible to me.
Just as a note, you often see key strengths described in bit length with RSA being 1024 or 2048 bits, and AES being 128 or 256 bits.
This might lead one to assume that RSA is much stronger that AES, but the opposite is true (at these key lengths). The problem is that the two systems are attacked in very different ways. AES is attacked by a brute force search through all possible keys until the right one is found. If the key is 256 bits long, then you need to try, on average, half of the 2^256 keys. That is about 10^77 keys (a whole lot). This attack is basically impossible for any computer that we can imagine being built, in any amount of time relevant to the human species (let alone any individual human).
By comparison, RSA is broken by factoring a 1024 or 2048 bit number in the key into its two prime factors. While very hard, it is not like brute force. It is generally thought that 1024 bit RSA is about as hard to crack as 80 bit symmetric encryption. Not all that hard.