The style of shapes can alter the look and feel of the application and thus change the user experience.
Apple got praise with their rounded corner movement showing that a different style shape can lead to a better User Experience. Lets look at examples
Which image is easier to follow?
Which Image would you prefer to look at (aka is easier on the eyes)
This is one of the best examples of how rounded corners or a different style shape can lead to a better user experience.
Those were taken from This article explaining why rounded corners are easier on the eyes
The following are some highlights of that article.
Lets compare rounded shapes to ones with Angular edges
Objects with pointed features, elicited stronger activations in the
region of the brain related to associative processing, meaning that
although angular objects were less liked they elicited a deeper level
of processing than did the contoured objects - they were in effect,
more interesting and more thought-provoking to look at
Angular objects are more effective at attracting attention and
engaging thought; contoured objects are more effective at making a
positive emotional and aesthetic impression.
The following two examples came from this similar question.
In regards to different types of shapes when they serve as buttons see the following
This [Article] provided some interesting insight.
- Make buttons look like buttons (ie the shapes people are used to seeing)
seem to be more button like than image below. (notice the shape difference)
How significant the shapes of objects are on altering the experience is much more difficult to measure though. I personally would do A/B tests with shape designs on amazon mechanical turk for a cheap and dirty way to see what people prefer.
Reading more about Contour Bias further describes some of these topics
Below are two images from that article
Contour bias is a tendency to favor objects with curved contours over objects with sharp angles or points. If you think about it on a subconscious level this makes a lot of sense. Sharp and pointed objects can be used to stab and cut. They are potential threats to us physically. They lead to an subconscious processing of fear in a region of the brain called the amygdala.