Great question! One of the most common things I see is people choosing art that's too small for their wall.
Although I don't have a single solution for every situation, I can share a few guidelines to put you on track in choosing a size that's likely to compliment your space.
Here's what I've found to work...
Over furniture
We're going to start with the most common place people hang art - over the couch, bed, chair, cabinet, dresser... you name it.
To begin, I recommend avoiding hanging artwork that's exactly the same width as the furniture below it. This can make an area look blocky (unless you're going for this look, of course).
In general, hanging a painting that's 2/3 to 3/4 the width of the furniture is pleasing to the eye.
If you are hanging more than one piece or a grouping of art, then the overall grouping will be 2/3 to 3/4 the width of the furniture below.

Paintings L-R: “Another Perfect Day” and “Perfect Day” by Theresa Edwards
In this example, the painting at left is hung a little low and is the same width as the cabinet creating the block effect I just mentioned.
The one at right has been raised to give visual resting space, and is 3/4 the width of the cabinet making for a more comfortable feel. A tall plant or floorlamp to the right would finish it off nicely.
No furniture? (no problem)
Maybe you're filling a hallway or transitional wall between rooms. I'd use the same formula by filling 2/3 to 3/4 the width of the wall space with art. Remember when hanging multiple pieces, use the width of the entire group.
Height of the ceiling
High ceilings can make the art on your wall feel smaller than it is. This means you could increase the height of a painting, adding a feeling of fullness or warmth to the room. On the flipside, if you have low ceilings, you may opt for a piece that's shorter in height.

Painting: “Into the Falls”
The painting above is 4 ft tall but could be even taller since the ceiling in this space is so high.
When in doubt, go big
I have to say that oversized art can look very cool...
It makes a statement and frankly, exudes confidence. It's very rare for someone to go overboard with this. In fact, with many people it's the exact opposite. They tend to undersize their art, creating a slightly barren look.

“Another Perfect Day”, 32×60 inches
This painting's not oversized, but a nice example of filling a wall without being timid!
If you're the adventurous type who's not afraid to go big, just be sure to leave a bit of space near the edge of any wall (never hang right to an edge or corner).
Oversized art breaks a lot of rules, but one thing I still recommend is to leave a little breathing room. Even if you were to create a gallery wall that fills your entire wall, you'd want to leave a margin of space around all edges.
Once again, big art makes a big impact. It can be wonderfully bold and expressive when you walk into a room. Just make sure you LOVE the large pieces you collect because there's no hiding them behind a plant lol.
If you're looking for big art for your walls, check out my gallery of large paintings.
Did any of these tips help you feel more confident in picking a size? Do you have other questions you'd like answered? Let me know in the comments.