Does concating a string like this open me up to SQL injection? I recently answered a question with the following code sample:

Create Table #Testing
(
  emaildomain varchar(100) -- Still bigger than functionally needed but better than MAX
);
INSERT INTO #Testing VALUES (REVERSE('@myfreepaysite.com')); -- Changed


Create Table #DataToCheck
(
  fullemail varchar(200) -- Still bigger than functionally needed but better than MAX
);
Insert Into #DataToCheck VALUES(REVERSE('rr1234@myfreepaysite.com')); --Changed

Select Top 1 
  REVERSE(fullemail)
  , REVERSE(emaildomain)
FROM #DataToCheck
  INNER JOIN #Testing ON fullemail LIKE emaildomain + '%';


As I was writing that last line I wondered if concating EmailDomain column with the wildcard symbol was an opening for SQL injection. Is this something I should watch out for this type of code or will SQL Server evaluate this as a single unified parameter so I don't need to worry about using this approach?
No. That value will always be interpreted as a string and there's no way to put anything into the emaildomain column that could make the query execute unexpected code. It's either going to find matches or it's not.

Of course, this is relevant to the specific code sample you posted, and only that. You should always be concerned about any data you accept from a user... since you might not know where else it might be used now or in the future.