Have you ever wondered how long it would take to create a 32768 bit RSA key with ssh-keygen? Well, I did.
$ time ssh-keygen -t rsa -b 32768 -f ~/.ssh/tmp32768 -N foobar -q real 244m31.259s user 244m15.664s sys 0m4.736s
In other words, on my test system (AMD X2 CPU with 1.8 GHz per core) it took ca. 4 hours. This is likely very dependent on how much entropy you can get (and how fast), so take the numbers with a grain of salt. A second key with 32767 bits (one less) took 16 hours, for instance.
The resulting tmp32768 (private key) file is ca. 25 KB big, the tmp32768.pub (public key) file is 5 KB big.
There's likely no noticeable performance hit for ssh or scp AFAICS, as all data transfers are done with a symmetrical session key, not the RSA key itself. Only the initial connection "handshake" will take ca. 40 seconds longer...
And yes, 32768 is the maximum RSA key size you can currently create with OpenSSH, go file a bug report if that's not enough for you ;-) However, as I then noticed, this key will not actually work. When you put it in some authorized_keys file and try to login, the handshake will fail and the server-side will see the following error in /var/log/auth.log:
sshd[xxxxxx]: error: RSA_public_decrypt failed: error:04067069:lib(4):func(103):reason(105)
I first thought I found an off-by-one error, but the 32767 bit key (one bit less) didn't work either. After looking through the OpenSSH and OpenSSL code as well as the RSA_private_decrypt(3SSL) manpage a bit, I saw that OpenSSH uses the RSA_PKCS1_PADDING parameter. My current theory is thus that some padding is making the key not work. I'm now creating a key with 11 bits less bits than 32768, let's see what happens. For the record, a key with 16384 bits does work just fine.
Anyway, I'll probably report this as "bug" (more a theoretical than a practical problem, though) as ssh-keygen let's you generate RSA keys which will never work in practice...