There are a number of universes in which Hulk can talk normally, but just considering Earth-616, we have a few.
Gray Hulk/Joe Fixit – The Gray Hulk (though not the original) worked for a time as a Las Vegas enforcer called "Joe Fixit". The Gray Hulk has poor intelligence, although he occasionally displays knowledge and intellectual ability normally associated with Banner.
Merged/Professor Hulk – The Merged Hulk is the merger of Banner and the Savage and Gray Hulks. The Merged Hulk was later retconned into The Professor. The Professor, rather than being a merger of the three main personalities, was interpreted as a fourth, separate personality that represented Banner's ideal self. The primary difference between the two is that the Merged Hulk demonstrated aspects of the Banner, Gray Hulk and Savage Hulk personalities (also possessing Banner's intelligence, Joe Fixit's cunning, and the Savage Hulk's size and strength), while the Professor did not.
World Breaker Hulk
World Breaker Hulk – The Hulk of World War Hulk is a cunning and more powerful version than the previous incarnations. His rage is at its most focused, due to meditation training by his ally Hiroim.
It should be noted that the other versions of the Hulk are generally described as having the intelligence and temperament of a child. He can talk, he just usually doesn't. These versions I mention (amongst others from across the multi-verse) are the ones that are as intelligent as, or more intelligent than a normal person.
In the MCU
Until recently, the Hulk has demonstrated very limited ability to speak. However, Thor Ragnarok changed this and depicts Hulk having entire conversations with Thor.