Remember, a pokemon combination is not really perfect. Any of these combinations I could break with the right moves and prediction. I could break an Electivire chain by predicting that you would switch and using Earthquake. I could predict that you would switch to Heatran and CC / EQ
Point taken, but this doesn't take away that in some cases, like Electivire + Gyarados, you don't have the option of using either one of those attacks. Electric + Ground is, as far as I know, quite a rare attacking combination.
Aside from that, using Earthquake while a Gyarados is out remains extremely dangerous, as you are allowing your opponent to stay in and get a free Dragon Dance up and running while you do basically nothing. Then again, using Thunderbolt is almost just as risky with Electivire being a potential switch-in, but this only works in your advantage: Your opponent will have to make a decision, and if he makes the wrong one, it can easily cost him the battle.
Back to the actual thread itself: just like Roy said, this thread isn't meant to be for 2 vs 2 discussion, it's about the standard 1 vs 1 battles, with the main idea being that when 2 of your pokemon are cooperating in a very solid way, you can easily switch between the two of them to avoid taking super effective damage. It has no use to put two pokemon who cover each other weaknesses very well together in a double battle, because the opponent would simply attack whichever one is weak to their attacks. And I think I made it perfectly clear with my initial post that this thread really isn't about 2 vs 2 battling at all, at least, the examples I gave with the introduction should indicate that.
Some additional things that should be kept in mind:
Pokemon that are both weak to a single type from a standard type combination (such as the previously posted Gliscor + Empoleon) aren't the best combinations possible, as you can't optimally switch between the two of them: a lot of pokemon still hit both of them with super effective damage. This way a main reason why I decided not to post Torterra + Heatran as an example, as the one is weak to Ice and the other to Water, both of which are commonly used together on Water pokemon.
It would come in handy if the pokemon you're building a combination around either resists Stealth Rock or only receive neutral damage from it (at max), as you don't want yourself to get into trouble when switching in and out.
The idea of Weezing and Spiritomb together sounded pretty nice.
Things that should also be considered are a Ghost pokemon and a Dark pokemon together, because as we all know thanks to Spiritomb and Sableye: Dark and Ghost together have no single weakness. This makes me think Umbreon and Dusknoir could effectively be used together, with one of them being focused on Def and the other on SpDef. My own preference would go to a physical-based Dusknoir and a special-based Umbreon, as Umbreon's only weaknesses are mostly physical ones (Fighting and Bug).
Dusknoir also has Will-O-Wisp to even further boost its physical defensive abilities, and it can help Umbreon when you're facing something that might carry a random physical attack (like many special sweepers nowadays pack Focus Punch).