Initial Discovery process I am looking to better my knowledge without actually being in the field, I was wondering what initial steps you take when you are assuming the responsibility of a server with SQL-Server installed on it. There are a few basics like hardware inventory, and permissions, backups. But what else do you do?
I did find some decent infromation on a few forums such as...

1. Backups


Ensure all db's are being backed up(system plus user dbs)
Ensure transaction logs backups are implemented where needed (check DB Recovery Models)
Check whether backups are native backups or 3rd party(ex. Red-Gate SQLBackups or Quest LiteSpeed)
Ensure to test the db backups on a test server using restores


2. SQL Jobs / Replication / Reporting Services / Analysis Services / Integration Services


Check on all and ensure functional


3. Logs


Check SQL Server Error Logs, Windows Logs for issues


4. Security


Server-Level Security, Services Security, Logins/Users Security, Audit Security, File System Security


5. Baseline the System


Use tools like Performance Monitor, SQL Profiler, Active SPID Performance


6. Implement a Monitoring, Alerting &amp; Performance Tool


www.sqlserverops.com, Microsoft Systems Center, www.idera.com, Quest, Red-Gate 


7. Implement a Change Control System for all Production Changes


all changes go through a process(request ticket, change ticket, approvals, deployments)
That is a great list. I would also use Brent Ozar Unlimited sp_Blitz, http://www.brentozar.com/first-aid/sql-server-downloads/. It will give you great overview of what might not be setup quite right.