Backgammon
Requires: A game board, 30 pieces {15 each in two colors}, dice, and a second human being.
Hardware Costs: We bought Backgammon for less then US$10.00 at Wal Mart. It was bundled with two other games, as well: Chess, and Checkers.
About: Backgammon is possibly the oldest strategy game in human history, with the possible exception of Go. In Backgammon, you place your pieces on the board and attempt to remove them from the board in a race against the other player. Of course, the game isn't nearly as simple as it first appears, and a person who is highly skilled in the game can cause your play to stop for better than half the game. But the game is not all about skill, as the dice add an element of luck to it as well. Sometimes, the dice just don't like you, and even the most skilled players can still be defeated by the rawest of newbies in Backgammon.
It is my humble opinion that Backgammon is in fact the best of all strategy games ever.
Chess
Requires: A game board, 32 pieces {16 pawns, 8 each in opposing colors; 4 rooks, 2 each in a opposing colors; 4 knights, 2 each in opposing colors; 4 bishops, 2 each in opposing colors; 2 queens, 1 each in opposing colors; 2 kings, 1 each in opposing colors}, and a second human being.
Hardware Costs: We bought Chess for less then US$10.00 at Wal Mart. It was bundled with two other games, as well: Backgammon, and Checkers.
About: For a long time, Chess took second place to Backgammon because unlike Backgammon, Chess is purely a game of skill. There is no luck involved, which means that as a rule, newbies don't stand a snowball's chance in hell. But then the Catholic Church ruled that any game involving dice was immoral, and suddenly Chess became the king of strategy games.
Chess is a wargame. You goal is to totally dominate your opponent, wipe out their army, and capture their king. The game has many vicious strategies and caveats, and even now, it seems impossible to know them all. If you are looking for a really good, very difficult game to master, Chess would be right up your alley.
Othello
Requires: A game board, up to 256 two-color pieces, and another human.
Hardware Costs: Othello can be purchased for less than US$30.00, I believe.

About: Not quite sure how to describe the game, but it's an excellent game with a lot of strategy involved. Your goal is to have as many pieces on the board as possible with your color turned up. As you place pieces of your color on the board, you turn pieces over so they are all your color.
The game appears to look something like Go, but Go is an entirely different game altogether. Go pieces are one color or the other, and do not flip. Also, go pieces can be removed from the board.
In Othello, you can not make a move if you can not flip any pieces. A great player can lock a person out of the game. An even greater player can win the game before the board is filled by making all the pieces their own color, thus eliminating all possibility of a move for their opponent.
This game ranks up there with Backgammon in my humble opinion.
You want great Video Games?
Space Invaders
Requires: Various. I think I first saw it on an Atari Game Console. In 1985.
Hardware Costs: This is generally freeware, anymore, without any hardware upgrades required if you're running anything newer than an 8086/8088.
About: Monsters are coming in to invade! You hide behind a bunker, riding back in forth in your tank, and blow them out of the sky before they land on your head!
This game is truly a great, classic shooter. Anyone who says it should use the full power of a US$10,000,000.00 PC must certainly be joking, because it's great even on an older PC.
PacMan
Requires: Anything newer than an 8086/8088.
Hardware Costs: As far as I know, it's available as freeware, now.
About: I was never any good at the game, but a lot of people seem to love the idea of being chased around mazes by a bunch of ghosts and eating everything in sight. The game is quite a marvel, and is truly one of the greats.
Conclusions
It becomes emminently clear that one does not need great hardware or great graphics or great special effects to have a great game. The most important aspect of a game is playability. The most important aspect of any environment is usability. Everything else should come second.