Cube decks vary a lot, mainly because of the fact that all cards are singletons. The most effective decks, however, typically follow an archetype. Archetypes are proven strategies that generalize a set of decks. They can be found in pretty much any format, from standard constructed to legacy constructed to booster draft. Some decks are primarily of one of these archetypes but may switch to another by changing how the cards are used, even in the middle of a match.
Beatdown decks try to win as fast as they can by using cheap aggressive creatures to overrun a slower opponent and take his 20 life before he can react. These decks focus on offense, often by giving up card advantage, life points and long term staying power. Good attackers, blocker removal and creature buffs are important for this archetype. At least half of the spells should be creatures for them to work.
Control decks are the opposite of aggro. They focus on surviving and growing until they subdue the opponent with powerful cards, so the cheap cards tend to be defensive, and the expensive ones, offensive. Essential components of a control deck are defense, diverse removal ("answers") and finishers. Card advantage spells like card draw, discard and mass removal are very desirable to have. Most spells should be about defense and a few should be finishers.
An aggro deck that starts offense early by setting up "clocks", that is, creatures taking life from the opponent. Then, it focuses on protecting that lead by killing or bouncing defenders, and discarding, countering or nullifying the opponent's removal somehow. Cheap creatures and midrange control are the base of this archetype. Fliers, shadow and unblockable creatures in general make great clocks. To protect them, counterspells are most effective, along with discard and untargetability effects. Reanimation and card draw helps to keep aggression and control coming.
Somewhat of a short-term control deck, which defends and ramps during the first turns, then proceeds to deploying a stream of medium to expensive attackers. Controlling the beginning is important against aggro decks, and having more threats than the opponent has answers is the way to go against control. Early defense and midgame offense are the core of midrange. Removal, counterspells, blockers, mass removal and bounce are good early control elements, while 4-6 cost creatures that have a big impact of the game are effective threats.
The most different of these five archetypes, combo aims to win by putting together a combination of cards that's very hard to beat. An example is Illusions of Grandeur + Donate, a combo in which you cast Illusions to gain 20 life and Donate it to the opponent. When he can't pay its upkeep cost, he'll lose 20 life. Combo is, by far, the hardest archetype to draft though. The singleton restriction already makes it nearly impossible, and if you focus on getting one combination, it's possible that not all cards will show up. Tutors, card drawing, card filtering and protection for your combo in the form of card draw and discard are necessary. It is also good to have some defense, as it is unlikely there you'll find too quickly your combo pieces.