The philosophy of midrange is that if you play more threats than your opponent has answers, the excess threats will beat him up to a pulp. These decks tend to have high average card power, as well as a high mana curve, relying on that sheer power rather than timing to win. It is very common to pack ramping cards, which help the big spells be cast earlier, as well as removal or tempo cards to delay the opponent's development.
A post by Ken Nagle that dates from 2007 about the midrange archetype can be read here.
Cube Decklist: WG Midrange
Constructed Decklist: Ghazi-Glare
Relative popularity in cube: Common
One of the most popular archetypes in my cube is WG Midrange. WG is the combination with arguably the most powerful creatures, so it's quite natural to tend to midrange when one drafts WG. At the beginning of the game, green provides mana acceleration and white provides defense and removal. Both colors have decent 4+ mana creatures, so putting together this kind of deck is typically easy.
WG is a combination that features a lot of life gain as well, which combined with the good defensive creatures that white and green have makes this archetype have a very solid matchup against aggro. However, it is usually vulnerable to spot and mass creature removal. It is not for WG Midrange to play around a deck packed with removal, but it can be done by running reliable finishers (like Myojin of Cleansing Fire), manlands (Treetop Village), equipment, or something else more creative (Stunted Growth, anyone?).
Rare Variation: WG Aggro
One approach to WG which is similar to midrange but not quite like it is aggro. The major difference is the mana curve and play pattern: while midrange will spend its first turns ramping, and then cast 4+ mana creatures, aggro will cast threats starting on turn 1 and pretty much ignore mana development. Both white and green have good offensive 1 and 2 mana creatures, which makes this a consistent aggro option. It is still weak to removal though, so equipment and manlands become even more important for this build to work well.
Cube Decklist: UG Midrange
Constructed Decklist: RUG Ramp
Relative popularity in cube: Common
This build works very differently than the previous. Blue is the opposite of white in terms of creature density, and acts as a support color for the green threats. The strategy is to let green focus on ramping and playing big monsters, while blue enabled it to do so. Typically, the deck will have some counterspells for disruption, some card drawing for refueling, and some tempo control to prevent the opponent from playing too fast to see your awesome fatties. This makes the deck less centered on playing big things, but it becomes way more versatile. UG does not have the raw power WG does. Rather, it can get out of any situation.
How this archetype plays varies a lot depending on the the decklist and the draw. The bulk of expensive threats will be green creatures, but don't assume blue will be restricted to the cheap part of the deck. It has a couple of good finishers as well, particularly evaders, and its creature control spells will often be game breaking.
Rare Variation: UG Control
If a UG midrange is too slow, it starts to lean towards UG control. Now, green is not a very appropriate color for control, as it does not have creature disruption. What it CAN do is play efficient blockers, ramp, cast Fogs, and make sure problematic artifacts and enchantments stay off the game. Green has a wide range of finisers though, making it a rare, but still viable choice as second color in a blue control deck.
If you are drafting a UG Midrange and notice it's leaning towards control (symptoms are: lack of ramping, lack of cheap tempo cards, presence of counterspells), then UG Control should be considered. It'll be a matter of strengthening the deck on the long run to make its plan A be "control the game completely then play finishers" instead of "play finishers as soon as possible".
Cube Decklist: BR Midrange
Constructed Decklist: Jund
Relative popularity in cube: Uncommon
Being the only color combination often used for midrange that doesn't involve green, BR obviously works with a different midrange paradigm. Black and red don't have especially good big effects. This is about how easy it is to use those two colors to control the opposition at the start of the game. Red kills creatures easily with burn, while black has discard and more creature removal. Burn and discard lose value as the game develops though, so it's natural to play some strong cards to try and close the game before the opponent recovers. This is exactly the play pattern of a midrange deck.
Some aspects of red and black can be used effectively in this build. Black reanimation, for example, works great to bring back the most problematic creature your opponent managed to deal with. High power low toughness red creatures work great as well, because the way will be open for them to close the game quickly. This color combination is good to create incremental card advantage. Look at Blightning, Blazing Specter, Murderous Redcap and Bituminous Blast. See a pattern there?
Rare Variation: BR Control
An archetype that just appeared once, but was so successful that I feel like it should appear sporadically. As stated above, black and red are very good in controlling the game early on, but lose efficiency at control in the long run. To circumvent that, cards that work well in a long game must be prioritized. This is the only archetype that did well with Goblin Charbelcher.
A weakness of this archetype is that it has a hard time dealing with enchantments. It is a narrow drawback, but really, when one plays a control deck, the games that go in their favor will take a while and most of their opponent's cards will be drawn. If the opposing deck has a single problematic enchantment, there will be in trouble. The biggest problem though, may be creatures immune to spot removal, such as ones with shroud, hexproof or indestructibility. Getting powerful mass removal is necessary to deal with those.
Cube Decklist: No register
Constructed Decklist: Dungrove Green
Relative popularity in cube: Rare
A rare build that takes the midrange game plan to its extreme, without other colors messing it up. This build is very consistent since it is monocolored and very focused. It's very unusual for the opponent to have blockers powerful enough to hold back a G Midrange offensive, but it suffers with its lack of versatility. Mass removal, counterspells and spot removal work well against it, making it a fragile archetype depending on what it's up against.
This deck comes together naturally when one is power drafting green. Its success, like any monocolored build, depends heavily on how many people are in that color, so it's an archetype that cannot show up in most drafts, but when it does, it's a serious contender that will wreck anything not prepared to stop a full-on creature offensive.