<p>When developing whether its Web or Desktop at which point should a developer switch from SQLite, MySQL, MS SQL, etc</p>

It depends on what you are doing. You might switch if:
You need more scalability or better performance - say from SQLite to SQL Server or Oracle.
You need access to more specific datatypes.
You need to support a customer that only runs a particular database.
You need better DBA tools.
Your application is using a different platform where your database no longer runs, or it's libraries do not run.
You have the ability/time/budget to actually make the change. Depending on the situation, the migration could be a bigger project than everything in the project up to that point. Migrations like these are great places to introduce inconsistencies, or to lose data, so a lot of care is required.
There are many more reasons for switching and it all depends on your requirements and the attributes of the databases.