Should the filtering column(s) always be in the keys / includes?

I'm considering creating a filtered index in my copy of the Stack Overflow database. Something like this, for example:

CREATE UNIQUE NONCLUSTERED INDEX IX_DisplayName_Filtered
    ON dbo.Users (DisplayName)
    WHERE Reputation > 400000;

Should I always add the column in the filtering expression (Reputation in this example) to the key or includes for the index, or is having it in the filtering expression good enough?

Yes!

For various reasons, it's always better to have the filtering column as part of the index: either in the keys, or in the includes

The following are some specific examples of filtered index query problems that are resolved by including the filtering columns in the index.
Key lookups when the query predicate doesn't match the filter expression

First of all, the documentation has this to say about including filter expression columns:

• A column in the filtered index expression should be a key or included column in the filtered index definition if the query predicate uses the column in a comparison that is not equivalent to the filtered index expression.

So if you have an inequality filter expression like Reputation > 400000, but your query uses a predicate like WHERE Reputation > 400000 AND Reputation

This might feel like it goes without saying, but just to be complete: if your queries include the filtering column in the final resultset, you should probably include them in the index (key or includes).
Poor row estimates when using equality expressions

There are cases where useful row estimates based on actual statistics can be eliminated during the optimization process (specifically when the query plan produced by the optimizer is converted to a physical execution plan). Including the filtering column can prevent these more-accurate estimates from being discarded.

More details, and an example, can be found in Paul White's answer on the now read-only Answers.SQLPerformance.com site: "Incorrect row estimation given with a filtered index" (Original Link | Wayback Machine)

An additional example can be found here on dba.se: Query using a filtered index but wrong estimated number of rows
Key lookups when using IS NULL in the filtering expression

Creating an index with a filtering expression that uses IS NULL` can produce a completely unnecessary key lookup. See this question, and the related bug report on SQL Server's feedback site: Why filtered index on IS NULL value is not used?

As you might have guessed, the workaround presented is to add the filtering column as an included column in the filtered index.

StackExchange Database Administrators Q#224149, answer score: 16