SQL Server Timeout: Gathering server side information We use SQL Server 2008 for our database. We use a combination of Classic ASP and .NET to connect to said database. We get random timeouts on queries that are extremely simple and when we run said queries they appear to be quick and have the correct indexes.

What I'm wondering is if there is a way to have SQL Server gather/keep data on these timeouts and send it to us. I've read in the past that you can do this for deadlocks.
Perhaps (at least some of) these "random timeouts" might be network related?

You should definitely consider performance monitor.  You can view statistics in real time, collect statistics to generate a baseline, and configure triggers to send alerts.

PS:
Here's a good link to get you started:

Free Microsoft Tools to Help Setup and Maintain PerfMon for SQL Server