Adding a filter to servers would be useful and help out when you're looking for a specific server or when you have too many servers sticking out in the list, like all the password protected servers
Why?: Cleans up the server listings, removes all the annoying password protected servers, more user friendly
The screenshots are just examples and not finished products
Filter to clear up some servers:

After the filters have been added, the servers 'filtered' out are still there, but in the top in drop down lists

I agree with this; what's the point of listing private servers if you can't entering them (only enabling to view them when you get the password)?
Because you enter the password on entering, and thus need to see them first?
Filtering is good, but it should keep showing all available servers.
@Gymnasiast Isn't picture number 2 better then? To have a 'Password protected servers' drop down list?
OR list all password protected servers in the bottom?
I'd say the following:
With more fine-grained options in the filter options.
This was fixed in 6acbfa0 with Gymnasiast request
Most helpful comment
I'd say the following:
With more fine-grained options in the filter options.