Implementing voting system like reddit/StackExchange?
What you have seems pretty solid.  How about 

create table vote (
   user_id int not null,
   content_id int not null,
   time_recorded datetime not null,
   vote int not null,
   primary key (user_id, content_id),
   foreign key (user_id) references `user`(user_id)
      on delete cascade,
   foreign key (content_id) references content(content_id)
      on delete cascade,
   check (vote = 1 or vote = -1)
);


A composite primary key with those two keys makes perfect sense.  They absolutely should be foreign keys as well.  I threw in to cascade a delete from the parent tables; if a user deletes, the "like" will be removed from the content (which, IIRC, is what happens in StackExchange), and if the content is removed, there is no real point in keeping the votes on it.  I also implemented the vote column as an integer which must be either 1 or -1, rather than a boolean.  That way you can get an overall tally of up and down votes with a simple sum(vote), rather than two select count(*).