Each card has a number of physical connections determining the number of cards that can be coupled. The CrossFire and SLI solutions are pretty much identical in this aspect.
While the current Nvidia drivers allow for SLI to work without the bridge connector, this puts some additional stress on the PCIe bus. If the cards have one connection each, two cards can be connected. If they have two, three or four cards can be teamed up using a three-way bridge connector or a four-way bridge connector.
The advantages of connecting cards with bridges have to be considered separately for AMD and Nvidia. You could easily leave the bridge connector off when using mainstream graphics cards, since the PCI Express bus is quick enough for the data traveling over it. This is only an option for certain AMD-based configurations, from a pair of Radeon HD 4650s down to two Radeon HD 4350s. Dip down into the Radeon HD 3000-series or up to Radeon HD 4670s, and you'll need to use bridge connectors.
If the graphics card has two CrossFire bridge connections, it doesn't matter if you use the left or the right one. Nor are there any advantages to using multiple bridge connectors between the cards just because you can. One is enough to synchronize the data stream and make the driver recognize the CrossFire configuration.