These are in no way exhaustive, but they cover a variety of different features.
The left and right columns should look identical - left uses a single background shorthand, and right uses separate properties.
background: url('background-repeat.png') fixed
background-image: url('background-repeat.png');
background-attachment: fixed;
background: url('background-repeat.png') local
background-image: url('background-repeat.png');
background-attachment: local;
background: url('background-repeat.png') scroll
background-image: url('background-repeat.png');
background-attachment: scroll;
background: url('background-repeat.png') bottom 5% right 10px no-repeat
background-image: url('background-repeat.png');
background-position: bottom 5% right 10px no;
background-repeat: no-repeat;
background: url('background-repeat.png') yellow padding-box content-box
background-image: url('background-repeat.png');
background-color: yellow;
background-origin: padding-box;
background-clip: content-box;
background: url('background-repeat.png') center / contain
background-image: url('background-repeat.png');
background-position: center;
background-size: contain;
background: url('background-repeat.png') center / cover
background-image: url('background-repeat.png');
background-position: center;
background-size: cover;
background: url('background-repeat.png') top / 50% 25px
background-image: url('background-repeat.png');
background-position: top;
background-size: 50% 25px;
See here for in-depth background-repeat tests.
background: url('background-repeat.png') space
background-image: url('background-repeat.png');
background-repeat: space;
background: url('background-repeat.png') round
background-image: url('background-repeat.png');
background-repeat: round;
background: url('background-repeat.png') space round
background-image: url('background-repeat.png');
background-repeat: space round;
background: url('background-repeat.png') no-repeat top 5px left 5px,
url('background-repeat.png') no-repeat top 5px right 5px,
url('background-repeat.png') no-repeat bottom 5px left 5px,
url('background-repeat.png') no-repeat bottom 5px right 5px,
url('background-repeat.png') no-repeat center cyan;
background-color: cyan;
background-repeat: no-repeat, no-repeat, no-repeat, no-repeat, no-repeat;
background-position: top 5px left 5px, top 5px right 5px, bottom 5px left 5px, bottom 5px right 5px, center;
background-image: url('background-repeat.png'), url('background-repeat.png'), url('background-repeat.png'), url('background-repeat.png'), url('background-repeat.png');