The main identifying characteristic of most contemporary rings is that they are made individually by hand, and are often signed and hallmarked by the artist. These can be made by anyone from the most prestigious top designers to local artisans featured at your town's outdoor market. The advantage to having an individually designed ring is that it will be made with care, devotion, and exquisite attention to detail. This is a guarantee of individuality as well as quality.
The latest styles in design and fashion hearken back to the golden age of Hollywood in elegant and romantic design (think of Audrey Hepburn or Grace Kelly), so contemporary interpretations of classic designs are very popular. One such example is the Lucida cut ring from Tiffany's, which pairs the classic diamond solitaire with a square-set princess cut diamond, lending a crisp geometric air to the classic design. Updating a classic style, especially one that emphasizes simplicity and elegance, is a good way to combine tradition with a fresh modern look.
It is also an increasingly popular trend to "recycle" old stones in new settings, for example setting the stones from an heirloom piece (such as your mother's wedding set) into a new band or setting. This way you can have exactly the ring you want, unique to you, and still reflect tradition and heritage. This can be done in a number of ways and with any combination of colors and stones. For example, in the instance of a second marriage where there are children involved, you may choose to combine the diamond engagement ring with a birthstone mother's ring. This shows the couple's commitment to the whole family. You can also "recycle" an old setting, whether it be a family heirloom or something remarkably beautiful that you found in the antique store, with repairs or new plating and a different stone. Any jeweler should be able to help you with these customizations.
Another favorite theme in contemporary rings is to combine colors of metal. This can be done with combinations of yellow, white and pink gold, Black Hills gold, silver and gold, yellow gold and platinum, and so on. This works well with barrel rings and patterns such as Celtic knots, modern "tribal" designs, and inlaid, scrollwork, or carved designs. This style adds contrast and visual interest, and is also adaptable with all styles of jewelry and clothing.
The best thing about a contemporary engagement ring is that it can be anything you want it to be, as simple or complex as you wish, cutting-edge or classic, any shape, size or color that you would like. You are limited only by your imagination; so shop around, have fun, and find (or create) the ring that is perfect for you.