What issues do I need to be aware of when I am deploying an ASP.NET application as a web farm?
All session state information would need to be replicated accross servers. The simplest way would be to use the MSSQL session state provider as noted.
Any disk access, such as dynamic files stored by users, would need to be on an area avialable to all servers. Such as by using some form of Network Attached storage. Script files, images and html etc would just be replicated on each server.
Attempting to store any information in the application object or to load information on application startup would need to be reviewed. The events would fire each time the user hit a new machine in the farm.
Machine keys across each server is a very big one as other people have suggested. You may also have problems if you are using ssl against an ip address rather than a domain.
You'll have to consider what load balancing strategy your going to go through as this could change your approach.