Domed rings

Danpasar Hero
Domed ring in sterling silver with 5ct citrine

Shyne jewelers
Diamond dome ring

The term domed refers to the bulgy shape of the ring as also seen with domed bands. in addition to the rounded profile a domed ring is usually tapered from narrow at the bottom to wider and higher at the top where stones can be set to highlight this focal point.

Ring sets

Attleboro Jewelers
Diamond wedding set in 14k white gold with 1/3ct princess cut center stone on the engagement ring and two pavé set half eternity bands

Sabrina Silver diamond wedding band set in sterling silver (rhodium plated)

Ring sets comprise two or more rings that can be worn together on the same finger often seen in this ring type are wedding sets i.e. engagement ring and wedding band.

Dress rings

Salna Jewellery
Multi band dress ring in 9ct white gold and pavé set diamonds

Dress ring with pavé set bow topper 

A dress ring is a ring; set apart from costume jewellery by it's use of precious materials, that is worn as an accessory without falling into the other categories of rings e.g. engagement rings, signet rings etc.

Engagement rings

Verragio
Engagement ring with pavé and rose gold accents

Novori
Engagement ring with side stones and trellis (cross over) setting in 14k white gold

An engagement ring is an indicator of marital status; in most of the western world wearing only an engagement ring on the third finger of one's left hand denotes that the person is engaged to be married. Once the wedding ceremony has taken place a common practice is to wear the wedding band exchanged during the ceremony on the same finger as the engagement ring.The middle of the 20th century saw a campaign by De Beers make diamonds a hallmark of engagement rings with their "A diamond is forever" campaign.

Costume rings

Miley Jewelry
Gold plated (zinc alloy) costume ring with pavé set zircon 

Vintage costume jewellery ring

Costume rings are made from non-precious materials and often imitate jewellery that would be very expensive if made from precious materials. The relative low cost and short life span of costume rings mean that they are ideal as a fashion accessory and the design trends of these rings can follow that of the clothing industry closely. Often seen in this type of ring are Strass stones which approximate the sparkle of diamonds; jewellery featuring this type of embellishment is sometimes referred to as paste jewellery because of the paste-like consistency of the glass flint material that is used to give the "stones" their sparkle.  

Eternity rings

Zoara
Prong set full eternity diamond ring in 14k white gold

David Dudley
Diamond set half eternity ring in 18k white gold

The eternity ring was brought into the market by De Beers as a way to shift smaller diamonds in larger numbers. A full eternity ring features a continuous line of identical stones all the way around the ring whilst a half eternity ring has the bottom section of the shank uncovered by stones to make it more comfortable to wear and cheaper to purchase.

Bands

Men's Tungsten steel band

Cartier
Wedding band in 18k pink gold

Bands in precious metals are commonly exchanged during wedding ceremonies and are characterised by their parallel sides. Bands in alternative materials are often worn as dress rings though they are distinct from other dress rings in their straight aspect when viewed in profile.Bands are usually made from a ribbon-like strip of material.

Signet Rings

Hollow gold signet ring in the British museum

Tiffany & Co 18k gold signet ring

Strictly speaking a signet ring is a ring that has engraving on the top, traditionally to impart insignia into wax or other seals to ensure security, the contemporary definition has expanded to include other rings that have the flattened top and broadening shoulders of the traditional signet ring even if no engraving is present

Cocktail Rings

Eragem cocktail ring in platinum with 12ct cushion cut aquamarine

Piaget cocktail ring in a style that resembles a cocktail drink

Cocktail rings were born during the prohibition era in America and typically feature a large central stone, usually bigger than 3ct. The idea behind the cocktail ring is that it is top heavy and is a way to flaunt that focal point.

Cluster Rings

Diamond Aurora  Halo cluster ring in platinum with 1ct center stone

Diamond cluster ring in 18ct white gold

A cluster ring is a ring that has focal point consisting of a cluster of stones sometimes with a larger stone in the center.

Solitaire Rings

Barkev
Solitaire ring in 14k white gold with 1ct round brilliant diamond.

Solitaire ring in 14k white gold with round brilliant cut diamond made in the Tiffany's style.

According to the oxford dictionary a solitaire ring is a ring holding only one stone.