There seems to be a constant debate among gaming hobbyists about direct negative interaction and how much should generally be allowed in a game, if any. The games that encourage it are labeled "Take That" games, as that is something your opponent might actually say to you when he gleefully slaps down a card to intentionally block you or otherwise impede your progress in the game. There are plenty of people who enjoy large doses of screwage in their games, but there are also those who will avoid such games at all costs, preferring what is often called "multi-player solitaire" games that allow each player to have his or her own "sandbox" that cannot be disturbed by opponents. These often feel like racing games, as each player is trying to solve the game's "puzzle" (i.e. reach a certain number of points through optimization) before his or her opponents.
Games that encourage negative interaction and those that exclude it have existed for some time. Pachisi and its more modern incarnations (Mensch Ärger Dich Nicht or Sorry!) are race games that allow players to send their opponents back to the beginning when they land on an occupied space. The Game of Goose, Snakes and Ladders, and Candyland, however are completely non-interactive and could easily "play themselves."
The development of modern boardgames during the last 50 years has seen an incredible increase in the variety of games of both types, as well as many varying degrees of interaction in between. I recently played Walnut Grove, for example, a game that has very little interaction at all. Then I played a older game by Wolfgang Kramer, one of the fathers of Eurogame design. His Viva Pamplona! was a hilarious romp through "take that"-style mechanics.
In fact, there are so many games being published of every kind these days, it seems pointless to argue vehemently for one particular style. There truly is something for everyone. There is still quite a bit of polarization, however, usually pitting fans of the so-called Eurogames (which generally have less direct interaction) against the so-called Ameritrash gamers (who generally prefer games in which a player can mess with another player's plans at any time during the game).
When it comes to game design, then, the subject of "target audience" becomes even more important, as this can determine the amount of negative interaction you will want to include in your game. If a "family game," for example, has too much negative interaction, it can cause hard feelings and encourage sibling rivalries. Too little, however, prevents the family from interacting in a meaningful way.
I usually design for the family market, and although I am not a huge fan of "take that" mechanics, direct interaction is very important to me. In fact, I have had several of my games described as "nasty," even though they are clearly Eurogames (90 minutes or less playing time, simple rules bordering on abstract). I'll take that as a good sign, and continue to strive for a middle ground.
The kind of negative interaction that should be avoided, however, is when a player unintentionally blocks or hurts an opponent by making a move that is in his or her best interest. This type of "accidental negative player interaction" is random and chaotic, making the game more frustrating.
The other kind of "take that" mechanic that I abhor is when a player must sacrifice a move that would improve his or her position in order to hinder an opponent. This often results in one player having to "take one for the team" in order to prevent another player from winning. The problem is, the player that does this weakens his or her own position, lessening the chances for victory and setting up a kingmaker problem.
Finally, I would obviously want to avoid a "take that" game that encourages targeting the weakest player (the easiest target). Even if the players begin the game on equal ground, once one player is weakened by another, the "feeding frenzy" begins, and that player can do little to prevent elimination from the contest. Multi-player war games are often susceptible to this kind of issue.
The ideal "take that" mechanic, then, is the type that:
1) can be intentionally directed at a specific opponent (and even better, a specific piece of your opponent's strategy)
2) does not force a player to sacrifice a move that improves his or her position
3) does not encourage targeting the weakest player
I'll call it, "You Take That! And I'll Take This!" and I believe that this is the kind of negative player interaction that can be positively received by the broadest audience.