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Essentially, you do need a speech tag if the reader can easily tell who is speaking. Under what conditions can the reader easily tell who is speaking:

1. There are only two people in the conversation and we know who spoke last, so the new speaker must be the other person. But note that you can't carry this on for too long or the reader will lose track, unless there is some other way for them to tell. 

2. The words could only be spoken by one character. This is by far the most powerful technique. If you have established to goals, manners, and speech patterns of each character so that in this particular conversation, only that character could possibly be the one to say those words, then you don't need a speech tag. 

3. There are other contextual clues to indicate who spoke (such as one character naming another, as has been mentioned). Inserting these artificially to avoid using a speech tag, however, would be a bad idea. 

Personally, I think that item 2 above is so important that it is a good test of the quality of your dialogue, and of your character building, that you can omit speech tags most of the time. It ought to be the case that every line of dialogue could only possibly be spoken by one characters. Making sure that that is true for your story is the best way to limit your reliance on speech tags.