You can separate paragraphs a number of ways.
Indents
Lorem ipsum dolor sit amet, consectetur adipiscing elit.
Curabitur in orci pellentesque, volutpat metus eget, interdum
mauris.
Nunc faucibus lectus id libero blandit, et varius augue
vehicula. Cras eu dictum libero, a elementum velit. Fusce
ultrices malesuada elit, et convallis massa tristique in.
Vivamus vel urna eget orci tincidunt luctus eget ac tortor.
Integer faucibus ante eu mauris faucibus, sit amet tincidunt
velit rhoncus. Proin a pellentesque nunc. Aliquam vitae neque
sit amet neque aliquam ultrices eget vitae urna.
Blank Line/Space
Lorem ipsum dolor sit amet, consectetur adipiscing elit.
Curabitur in orci pellentesque, volutpat metus eget, interdum
mauris.
Nunc faucibus lectus id libero blandit, et varius augue
vehicula. Cras eu dictum libero, a elementum velit. Fusce
ultrices malesuada elit, et convallis massa tristique in.
Vivamus vel urna eget orci tincidunt luctus eget ac tortor.
Integer faucibus ante eu mauris faucibus, sit amet tincidunt
velit rhoncus. Proin a pellentesque nunc. Aliquam vitae neque
sit amet neque aliquam ultrices eget vitae urna.
Fleurons/Flourishes/icons/bugs
Lorem ipsum dolor sit amet, consectetur adipiscing elit.
Curabitur in orci pellentesque, volutpat metus eget, interdum
mauris. ~•~ Nunc faucibus lectus id libero blandit, et varius
augue vehicula. Cras eu dictum libero, a elementum velit. Fusce
ultrices malesuada elit, et convallis massa tristique in. ~•~
Vivamus vel urna eget orci tincidunt luctus eget ac tortor.
Integer faucibus ante eu mauris faucibus, sit amet tincidunt
velit rhoncus. Proin a pellentesque nunc. Aliquam vitae neque
sit amet neque aliquam ultrices eget vitae urna.
Numbers
1 Lorem ipsum dolor sit amet, consectetur adipiscing elit.
Curabitur in orci pellentesque, volutpat metus eget, interdum
mauris.
2 Nunc faucibus lectus id libero blandit, et varius augue
vehicula. Cras eu dictum libero, a elementum velit. Fusce
ultrices malesuada elit, et convallis massa tristique in.
3 Vivamus vel urna eget orci tincidunt luctus eget ac tortor.
Integer faucibus ante eu mauris faucibus, sit amet tincidunt
velit rhoncus. Proin a pellentesque nunc. Aliquam vitae neque
sit amet neque aliquam ultrices eget vitae urna.
All (as well as other methods) are all valid. What's usually frowned upon is combining them, as it's a bit redundant. If you already have a space between paragraphs, indenting isn't really going to help separate them visually.
As for why you usually see blank lines/space as the primary way to separate paragraphs on the web it's because that's just the default. By default, most browsers traditionally added space between <p>
tags. So there was just no need to use indents. But you are certainly free to use indents if you'd prefer.