Grab the latest version of Nginx, turn on SPDY, enable SSL session cache.
You must always serve your API over SSL, as auth information is going to be in headers or the querystring and both would be readable by a MITM if you do not use SSL.
Nginx 1.4 statements to pay attention to (sample config):
ssl on;
ssl_certificate /etc/ssl/domain.crt;
ssl_certificate_key /etc/ssl/domain.key;
ssl_session_cache shared:SSL:10m;
ssl_session_timeout 10m;
ssl_ciphers RC4:HIGH:!aNULL:!MD5;
ssl_prefer_server_ciphers on;
ssl_stapling on;
spdy_headers_comp 1;
If you're not using Nginx, why not? Just use it as a reverse proxy and drop it in front of whatever you are using.