With Blender 2.8+ you can use the *Auto Merge* Tool to insert a vertex between intersecting edges.

[![enter image description here][1]][1]

Just enable the option *Auto Merge* and *Split Edges & Faces* in the Tool Shelf, then select a vertex and move it. Upon placing it down the tool will create vertices between the connected edges and the edges intersecting them.

If you don't want to move any vertices just select one, press <kbd>G</kbd> to move and confirm with left click without altering the position.

  [1]: https://i.sstatic.net/VMMFD.png