Is there an operator or an easy way to match an expression one or more times with the LIKE operator in SQL?
If you are talking about solving this purely in Transact-SQL, you can cover all those cases in your example data with the following filter:

WHERE FilteredField LIKE '%[a-zA-Z][0-9]'


If you want to additionally stipulate that all the characters before the numeral must be Latin letters, you will need to get a little creative:

WHERE FilteredField     LIKE           '%[a-zA-Z][0-9]'
  AND FilteredField NOT LIKE '%[^a-zA-Z]%[a-zA-Z][0-9]'


Basically, you are saying:


  The value must end with a letter and a numeral, but whatever precedes the letter must not be a non-letter.


There is no way to specify this with a single condition using only built-in syntax, if that was what you were after.