There are currently 18 different types in Pokemon, with the most recent added in Generation VI.
The first new types added to Pokemon were Dark and Steel in Generation II. No new ones were added until the Fairy-typing came along. Yes, there was a "???" type, but no one really counts that.
It is uncertain if Pokemon will introduce a new type or two any time soon. The types seem pretty set in stone. If they do add some new type categories though, there are a handful of cool ideas they could put into place.
Note: This article is subjective and reflects the opinion of the writer.
Top 5 ideas for new Pokemon types
#5 - Cosmic
Cosmic-type Pokemon would be those with an affiliation to space. A lot of Legendary Pokemon come from space, as well as the Clefairy evolutionary line. Yes, they were made Fairy-types when it was introduced, but Pokemon has never been shy about changing things up. The likes of Deoxys and Lunatone/Solrock could easily become Cosmic-types.
#4 - Tech
The Tech-type could give a specific type to the mechanical and technology Pokemon of the series. There are several which seem to be like computers or machines. These include the Porygon line, as well as Rotom. More machine-like Pokemon could be added to the series to really bulk up the roster of Tech-types.
#3 - Light
Many Pokemon fans are surprised that a Light-type category has never been added. It was almost a sure thing once the Dark-typing was introduced. There are a lot of Normal-type Pokemon that could fit this category. Arceus is a perfect example. Unfortunately, some believe it would be too close to Fairy for it to ever become a real thing.
#2 - Peaceful
Peaceful would be another opposite to the Fighting-type category. While Fighting-type Pokemon are known for being brutal battlers with incredible physical strength, Peaceful would be the counter. There are Psychic-types that do this already, but Peaceful-type Pokemon would focus on defensive strategies and defeating Pokemon in battle with non-violent tactics.
#1 - Sound
Sound may be the most requested type that has never entered the Pokemon series. In fact, a recent fan-made game known as Xenoverse included the Sound-typing in it. Pokemon like Exploud, Chatot, and even adding a third typing to Toxtricity, would see the start of the Sound-type. There are already a ton of moves that are classified as "sound-based." This would fit the franchise perfectly.