There are five films based on the Hannibal Lecter novels by Thomas Harris, but the four that make up the film series are The Silence of the Lambs, Hannibal, Red Dragon, and Hannibal Rising. The other film, Manhunter, is also based on Harris' novel Red Dragon, but most people don’t consider it to be a key “Hannibal Lecter movie” as it uses different actors, and the film's producers never obtained the copyright to use the name “Hannibal Lecter” (“Lecktor” is used instead).
In order of release, the Hannibal Lecter films are:
1. The Silence of the Lambs (1991)
2. Hannibal (2001)
3. Red Dragon (2002)
4. Hannibal Rising (2007)
You can also watch the films in order of events, which would be:
1. Hannibal Rising (2007)
2. Red Dragon (2002)
3. Silence of the Lambs (1991)
4. Hannibal (2001)
Personally, I don’t really think it matters which order you watch them in, but The Silence of the Lambs is the most popular, so it might be a good idea to start with that one to see if you want to watch the others.
When it comes to Hannibal, I’d recommend reading the book, as the ending is far more interesting!