What variants are there for the playing-card-based game "War"?
There is a variant of war, called "Strategy War" or "Armed War" (a joke on hands) where, instead of pulling the card from the top of your deck, you chose it from your hand.  This works as follows:


You shuffle the deck and deal it out in equal parts.  Each player takes the cards dealt to him/her and puts them in his/her hand.
All cards a player plays and all cards a player gains during the game go to his/her discard.
A player's discard becomes his/her hand only upon his/her hand becoming empty.
War is played as usual, but with players choosing which card to play from their hands instead just pulling off the top of their pile.  Players each play their card face down, and then once all cards are down, players reveal the cards they have played.
In the event of a WAR, players shuffle their hands and take three cards at random from their hand to form the facedown "WAR" cards, then return to viewing their hands to select the final card for the WAR.  If, during this process, a player does not have enough cards in his/her hand, he/she puts all the cards from his/her hand into play as "WAR" cards, then continues using cards at random from his/her discard to complete the three facedown cards, then takes his/her remaining discard as his/her hand and continues playing.
2's beat whatever card is highest (Aces, unless you are playing with Jokers), but lose to all other cards.  This is essential in this variant, to make Aces not just an obvious play at the end of a war.


For example, players Aaron and Blake each play a card face down; they reveal, both showing a King.  They shuffle their hands, each put three cards at random from their hands into play facedown, and then return to their hands to select a final card for the WAR.  When they reveal the final card, Aaron played an Ace and Blake played a Queen; Aaron wins the whole hand and takes all 10 cards.

The advantages to this variant are several fold.  First, there is actual strategy.  Second, wars are more common due to the overlap in play style.  Third, there are interesting tradeoffs between using your best cards early versus saving them for later, which is a great thing for kids to learn.

If you want to make the game faster, take out a chunk of the low-valued cards, such as the 3's through 8's (make sure to keep the 2's as the ace-beaters).