Does Dapper support the like operator?

Try:

term = "whateverterm";
var encodeForLike = term => term.Replace("[", "[[]").Replace("%", "[%]");

string term = "%" + encodeForLike(term) + "%";
var data = conn.Query(@"
   select top 25 
  Term as Label, 
  Type, 
  ID 
  from SearchTerms 
  WHERE Term like @term", 
  new { term });

There is nothing special about like operators, you never want your params inside string literals, they will not work, instead they will be interpreted as a string.

note

The hard-coded example in your second snippet is strongly discouraged, besides being a huge problem with sql injection, it can cause dapper to leak.

caveat

Any like match that is leading with a wildcard is not SARGable, which means it is slow and will require an index scan.