Is there any limit to the number of databases you can put on one SQL server? I'm setting up a SaaS system, where we're planning to give each customer their own database. The system is already set up so that we can easily scale out to additional servers if the load becomes too great; we're hoping to have thousands, or even tens of thousands of customers.
Questions

Is there any practical limitation on the number of micro-databases you can/should have on one SQL Server?
Can it affect performance of the server?
Is it better to have 10,000 databases of 100 MB each, or one database of 1 TB?

Additional information
When I say &quot;micro-databases&quot;, I don't really mean &quot;micro&quot;; I just mean that we're aiming for thousands of customers, so each individual database would only be a thousandth or less of the total data storage. In reality, each database would be around the 100MB mark, depending on how much usage it gets.
The main reason to use 10,000 databases is for scalability. Fact is, V1 of the system has one database, and we have had some uncomfortable moments when the DB was straining under the load.
It was straining CPU, memory, I/O - all of the above. Even though we fixed those problems, they made us realize that at some point, even with the best indexing in the world, if we're as successful as we hope to be, we simply can't put all our data in one big honkin' database. So for V2 we're sharding, so we can split the load between multiple DB servers.
I've spent the last year developing this sharded solution. It's one license per server, but anyway that's taken care of since we're using VMs on Azure. Reason the question comes up now is because previously we were offering only to large institutions and setting up each one ourselves. Our next order of business is a self-service model where anyone with a browser can sign up and create their own database. Their databases will be much smaller and much more numerous than the large institutions.
We tried Azure SQL Database Elastic Pools. Performance was very disappointing, so we switched back to regular VMs.
I've worked on SQL Servers with 8 to 10 thousand databases on a single instance.  It's not pretty.  

Restarting the server can take as long as an hour or more.  Think about the recovery process for 10,000 databases.

You cannot use SQL Server Management Studio to reliably locate a database in the Object Explorer.  

Backups are a nightmare, since for backups to be worthwhile you need to have a workable disaster recovery solution in place.  Hopefully your team is great at scripting everything.

You start doing things like naming databases with numbers, like M01022, and T9945.  Trying to make sure you're working in the correct database, e.g. M001022 instead of M01022, can be maddening.

Allocating memory for that many databases can be excruciating; SQL Server ends up doing a lot of I/O, which can be a real drag on performance.  Consider a system that records carbon use details across 4 tables for 10,000 companies.  If you do that in one database, you only need 4 tables; if you do that in 10,000 databases, all of sudden you need 40,000 tables in memory.  The overhead of dealing with that number of tables in memory is substantial.  Any query you design that will be ran against those tables will require at least 10,000 plans in the plan cache if there are 10,000 databases in use.

The list above is just a small sampling of problems you'll need to plan for when operating at that kind of scale.

You'll probably run into things like the SQL Server Service taking a very long time to start up, which can cause Service Controller errors.  You can increase the service startup time yourself, create the following registry entry:

Subkey: HKEY_LOCAL_MACHINE\SYSTEM\CurrentControlSet\Control
Name:   ServicesPipeTimeout
Type:   REG_DWORD
Data:   The number of milliseconds before timeout occurs during service startup

For example, to wait 600 seconds (10 minutes) before the service times out, type 600000.



Since writing my answer I've realized the question is talking about Azure.  Perhaps doing this on SQL Database is not so problematic; perhaps it is more problematic.  Personally, I'd probably design a system using a single database, perhaps sharded vertically across multiple servers, but certainly not one-database-per-customer.