Balloon Fight was developed by Nintendo and published in the US for the NES in 1985. While the game is uncommon (as of this noding) due to the fact that it was an NES launch title, an utter lack of demand coupled with the e-Reader availability has driven the value down to only a few dollars. (The box and game label are simple, with a picture of the gameplay on a black label, with "Balloon Fight" in yellow letters, the "Nintendo Seal of Approval", and the "Arcade" category label common on early ports of NES games from the Vs. Unisystem.
(Some of this info is courtesy of TheBooBooKitty.) Balloon Fight, released in 1984, was yet another Vs. Unisystem game, usually displayed in unadorned cabinets. The gameplay lacked the Balloon Trip mode below, and the attract mode was unremarkable.
Balloon Fight, due to its simple, addictive gameplay (and VERY small size, as the game is under 45K) has been one of the games Nintendo has been pulling out as they mine their archives. It was rereleased on September 17, 2002 as one of the games in the first series of cards for the Nintendo e-Reader for the Game Boy Advance, and Balloon Fight is one of the common NES games in Animal Crossing (released September 16, 2002).
The ROM is fairly rare due to obscurity, but it's very small and very complete, and should run in even the most limited emulators (as it uses the most basic possible mapper.)
The intrepid Balloon Fighter was also immortalized as a trophy in Super Smash Bros. Melee, and the theme music is available as an alternate theme for the Ice Climbers stage.
Rather than having a "Game A" and a "Game B", which differ only in difficulty (as in many of Nintendo's ports of its arcade games of the time) the game had a "Balloon Trip" mode in addition to the main game, one which offered a game quite different from the arcade experience.
The gameplay itself is probably the least interesting thing about this game from a historical point of view, as Balloon Fight seems largely derivative of the Williams classic, Joust. The nameless hero, armed only with a pair of balloons and a pin, is recrited to go out and fight the inexplicable attack by equally inexplicable foes floating around on balloons. The gameplay is simple, as you need to just ram your opponents from above, breaking their balloons, then stomp on them when they land or ram them from above, ripping their parachutes. The latter is worth more points. An aggressive fish in the water will attack you or your enemies if you get too close, and the clouds will shoot bouncing lightning bolts that will kill you if you touch them.
The two-player mode was competitive, as players could burst each other's balloons as they fended off the computer balloon fighters. Not only that, but bursting your opponent's balloons would score you points, encouraging cutthroat play.
Balloon Trip, exclusive to the home versions, was a little different. You had to manuever around a sidescrolling (right to left, interestingly) course of stationary and moving lightning bolts, popping each of the free-floating balloons. You were only given one life, so one mistake would end your trip, but there was no penalty, other than missed points, for not popping balloons. Bonus points could be earned for perfect streaks of popped balloons.
Balloon Fight, like many of Nintendo's early hits, also found its way into Nintendo's Game and Watch line of portable LCD games. Released in November 1986 in the Crystal Screen line, it's notable for how well it holds to the original game (as well as any LCD version of pinball holds up, for comparison) as well as the fact that it had no Japanese release. This game is quite rare, and can bring upwards of $50, depending on condition and packaging.
See also the Japan-only Game Boy Color enhancement/sequel in Balloon Fight GB.
Sources: TheBooBooKitty, the Killer List of Video Games, GameFAQs, Nintendo.com, the e-Reader cards