Why do we like paintings?

Why do we like certain paintings? is it the colors? the lines? Or is it the composition? Composition is one of the most important things in artwork, arguably the single most important thing because; it dictates what's in the painting, where the subjects are located, and tells the viewer where to look.

Autumn Leaves, Yokoyama Taikan, 1931, From the collection of: Adachi Museum of Art
In this painting the subject is stands out in the composition of the piece for two main reasons; size and color. The red tree stands out against the cool, blue background and it also occupies most of the painting, without overwhelming the viewer. Another noticeable principle of the painting is that the tree occupies 2/3 of the canvas in the horizontal plane.
In this piece the art a lot more subtle, faded and calm, yet the birds are represented in a bold black color to contrast with the background.The subjects of this painting are also located 2/3 of the way from right to left, which lends to more visual interest.
The 3rd Japanese painting depicts several characters on board of a small boat that occupies most of its composition. We can get a clue of who are the most important subjects in the artwork because they are represented with more saturated colors that contrasts with the other characters, as well as the background of the painting.
Elijah and the Chariot from Our Historical Heritage, Salvador Dali, 1975, From the collection of: SCAD Museum of Art
In this painting, lines play a big role because there are only a few shapes represented by solid colors. Furthermore, there is a subtle direction towards the main subject by the sun's rays.
Architect’s Dream, Thomas Cole, 1840, From the collection of: The Toledo Museum of Art
Like every other Hudson River School painting, awe inspiring landscape and dramatic lighting is the main attraction. But there are many other reasons why these paintings are very attractive to the eye of the viewer. Perspective plays one of the big roles in these types of paintings, as well as the mind-blowing proportions of the landscapes they depict.
Views Across Frenchman's Bay from Mt. Desert Island, After a Squall, Thomas Cole (American, b.1801, d.1848), 1845, From the collection of: Cincinnati Art Museum
In this case, the composition attracts the viewer because of a perfect use of the Rule of Thirds; dividing sea and sky right at the 2/3 mark from top to bottom as well as from left to right (1/3) with the rocks and the splash of the waves which play an important role in terms of movement in this painting.
The great battle at Lushunkou (Ryojunko fukin daigekisen), Adachi GINKO, 1894, From the collection of: Art Gallery of South Australia
Again, another perfect example in the use of Rule of Thirds in a composition with the mounted soldier and smoke occupying 2/3 of the painting from right to left chasing away the losing samurai on the remaining third in the composition. There is also an interesting use in color on the winning soldiers contrasting with the dark and more muted tones of the background and samurai.
Study of Two Warriors' Heads for the Battle of Anghiari, Leonardo da Vinci, ca. 1504–1505, From the collection of: Museum of Fine Arts, Budapest
Studies of Horses' Legs, Leonardo da Vinci, ca. 1490, From the collection of: Museum of Fine Arts, Budapest
This particular study is very attractive because of the movement in the horse legs. They also occupy most of the composition yet, they don't overwhelm the viewer.  Although there is no use of color, the use of Chiaroscuro makes this drawings very realistic and interesting.
Head of Leda, Leonardo da Vinci, c.1504 - c.1506, From the collection of: Royal Collection Trust, UK
The drawing represents a woman yet what makes this particularly interesting is the shape and lines created by the woman's dark hair against the background.
The Starry Night, Vincent van Gogh, 1889, From the collection of: MoMA The Museum of Modern Art
Just like in many of Van Gogh's paintings, movement is a big player in his compositions. The contrast between the big, bright stars and the dark landmarks also makes the viewers a lot more interested in this composition.
Self-Portrait, Vincent van Gogh, 1889, From the collection of: Musée d’Orsay, Paris
In this self-portrait, Van Gogh shows a perfect use of Rule of Thirds, placing himself 2/3 of the way in the composition. His red hair and beard also give more interest to the painting since they directly complement the muted blues and grays in the painting.
The Balcony Room, Adolph Menzel, 1845, From the collection of: Alte Nationalgalerie, Staatliche Museen zu Berlin
A painting that shows perspective to it's advantage is always interesting, and here it is very obvious that it plays the bigger role because; there is no subject. Simply an interesting use of lighting, movement and perspective makes this painting an enjoyable composition.
We inhabit the corrosive littoral of habit, James Gleeson, 1940, From the collection of: National Gallery of Victoria
Surrealism has something interesting to show because it always depicts something that we don't usually see. However these paintings also have more than meets the eye in terms of their composition, and how they attract the viewer. In this particular one, the movement of the drape on the floor, as well as the interesting proportions of the face contrasting with the body to the right, and at the same time; both of these contrast in color with the background.
The attitude of lightning towards a lady-mountain, James GLEESON, 1939, From the collection of: National Gallery of Australia, Canberra
In this Surreal painting, color is very saturated and contrasting. The soft skin-like tones perfectly complement the dark and vivid blues and greens from the background. Light has also a big role in this composition since the shadows create more visual interest that what is already there.