One of my favorite things about AsciiDoc is the ability to have each table element on its own line. E.g.
[cols=3, stripes=even]
|===
| x13
| x23
| x33
// new row
| x12
| x22
| x32
// new row
| x11
| x21
| x31
|===
Is something similar possible in Markdown (say Github-flavored-markdown)?
No this is not supported by any Markdown implementations that I am aware of.
Tables are a non-standard feature of Markdown and each implementation of them is different. However, you tagged this [github-flavored-markdown]
and Github has provided a spec for their implementation of the tables extension. While the spec does not directly state whether all cells of a row must be on one line or not, it does state the following (right before Example 204):
The remainder of the table’s rows may vary in the number of cells. If there are a number of cells fewer than the number of cells in the header row, empty cells are inserted.
That certainly implies that all cells must be on the same line. And the fact that there is no explanation or examples demonstrating how to split a row across multiple lines suggests that that is not a supported feature.