Token Ring is a clever but rather unpopular network technology.
Getzburg, in his above writeup, is right. Token Ring is better that Ethernet under heavy load.
Ethernet operates in Broadcast mode, and although it uses collision detection, it does not have facility to avoid collisions. Essentially, any NIC (Network Interface Card) may broadcast a signal onto the bus (first listening to ensure that no-one else is currently transmitting). Often, another machine on the network will decide to do the same thing at the same time, so next the network card listens to see if its transmission has collided with another. If it did, they both stop, and use a protocol called Binary Exponential Backoff. That means iterations of waiting a random amount of time before go through the process mentioned above. If collision occurs again they exponentially increase the maximum wait period (up to 14 iteration on Ethernet I think, when it just gives up, telling the layer above that transmission was not possible.
See Rancid Pickle's How Network Adapters Work for a good discussion of the NIC.
So, Ethernet does not guarantee transmission. In heavily loaded networks these collisions become a serious problem, and the network soon becomes saturated with collisions.
How is Token Ring different?
Well, in Token Ring, there is a token. Only the machine with the Token may transmit. This is collision avoidance. While a station is transmitting, it holds the token and no-one else on the ring can transmit. After that station is finished, and the last frame makes a complete ciruit of the ring, the Token is passed on; everyone gets a chance to transmit eventually and the problem of collision is avoided.
There is also all kinds of complicated shit to do with priorities, requesting the token, and beaconing which I'm not going into here. You can look it up if you really want. The data is still broadcast to everyone on the ring (see: Network Topologies) although, as with Ethernet, only the NIC to whom it is addressed need read it. Each machine on the ring accepts the frame, passing it to the next logical machine in the ring.
What about speeds and price?
Traditionally, Token Ring is slow. Up until a couple of years ago, you had a choice of 4 or 16 Mbps (while Ethernet was happily operating at 100 Mbps. Today, 100 Mbps Token Ring exists, but Ethernet is up to 1 Gigabit. Plus, as someone already mentioned in this node, Ethernet is cheap.
Hence, Token Ring is clever, yet unpopular.