Populate a SQL Server column with a sequential number not using an identity

I have a database table that has a lot of data already in the table and I need to add a new column to this table to include a new sequential number. In addition to adding the column I also need to populate the existing records with an incremental counter what options are there to do this?

SQL Server Sequence Numbers

In this tip we look at the Sequence Number feature in SQL Server and compare it to the use of identity columns.

How to Eliminate Gaps in Identity Values in SQL Server by Disabling the Identity Cache

Learn how to remove gaps in Identity values in SQL Server caused by Identity Cache.

How to Monitor IDENTITY columns to prevent unplanned downtime

If a table runs out of IDENTITY values then it, and any dependent services and applications, will be "read-only" until the problem is fixed. Steve Jones explains how to set up a custom monitor to detect and prevent such problems.

IDENTITY_INSERT