High availability websites

You can store session data in a database instead, which gets around that problem, then you can round-robin the requests to the application servers.

(Good) Load Balancers can be configured to be "sticky" which means they send requests from the same IP to the same server each time.

Loadbalancers. They should be configured in such a way that they can handle the sessions. Maybe by sending the same ip to the same backend every time. Or store them inside a database, or some shared memory if it needs to be really fast for some reason i haven't thought of.

Even if you have a load balancer sitting infront of two backend webservers, you just move the single point of failure onto the load balancer instead of the webserver. So your application would still not be highly available.

I highly recommend using a load balancer and at least a pair of web servers. At work, we use HA Proxy, which is fully capable of ensuring sessions are 'sticky', and are sent to the same web server unless it goes down, where it will fail over.

To make your load balancer highly available, you can set up two load balancing servers which are a mirror image of each other. Assign a single virtual IP to both of your load balancers. Write a script that will poll the other server to check if it's down; if it's down, have that script pick up that virtual IP address. The script should be running on both servers.

This link describes one way of managing a virtual IP address. Similar articles have been written for a large number of linux distros, but they are all based on the same method.