They provoke thought
A good painting should be able to get you thinking. Paintings are an artist's way of conveying their thoughts, opinions and ideas to the world. The artist should be able to effectively convey their message through the painting to the viewer. A good painting should therefore be able to tell the viewer what the artist was thinking and feeling when they created it. Painting should leave lasting impressions on you; they should get you asking questions and thinking about things you might otherwise have not asked or thought about.
They draw you in
A good painting should stand out from the rest. It should have something about it that attracts your curiosity and draws you in. It should command your attention and captivate you so that you spend lots of time admiring it and all of its features. Paintings of quality should reach out to you and grab your attention away from any other paintings that might be in the vicinity.
They showcase the artist's talent
A good painting should be a display of the artist's technical expertise. The painter should know exactly what they're doing and should be able to use the tools and tricks at their disposal to successfully create their work. With abstract paintings, there may not be as much skill or technical expertise showcased in the painting, though the artist still knows exactly what they're doing.
They're original
A good painting should have some level of originality to it. Of course, it's incredibly difficult to be truly original these days seeing as so many artists with great idea have passed before us. However, it's still possible to give your paintings an original touch that will make it stand out from others. A good painting shouldn't be generic: it should belong to the artist who painted it in the sense that the artist has left their mark on it.
They have a sense of harmony
A good painting should be consistent. The different elements that make up the painting should be of a similar style, nature and tone. These elements should complement one another to create a sense of balance and harmony in the painting. People prefer paintings where there's a sense of unity and the different elements are part of a single piece. People find balance and harmony more appealing and easy on the eye than chaos and discord. Many paintings that have less balance and more discord can make for good art, though. It's all subjective, of course.