How to use Powershell Where-Object like an IN statement

Powershell has an -in operator since Powershell 3

$srv.Databases | where Name -in "master","model","msdb" | write-output { $_.Name }

Further Reading: Docs on Comparison Operators > Containment Operators

Use the -contains operator. Like:

$dbs = "testDB", "master", "model", "msdb"

foreach ($db in ($svr.Databases | where-object {$dbs -contains $_.name  } )) {
    write-output $db.name
}

Use help about_Comparison_Operators to learn more about this and other comparison operators.

Update:

PowerShell v3 has added the -in operator. The example in the original question will work in v3.

You can use a regex:

$svr.Databases | where { $_.name -match 'testDB|master|model|msdb' } | foreach { $db.name }