Remove Cilantro Stems?
The stems are edible and flavorful, with a crunch that may or may not be desirable in your dish,  but the lower portion of them tends to be a little stringy.  I always trim off the bottom,  but as for the rest of the stem,  it depends on what I am making.

For raw dishes where it is chopped quite finely (koshimbir, pico de gallo) or even ground to a paste (chutney), or if there are other crunchy textured ingredients,  I will chop and include the stem (the middle to upper part, where there are also leaves branching off, or as much of it seems tender).

If I am cooking it (as a seasoning in a soup or dal) or if it will be wilted and steamed as it is tossed with a hot dish, then it is also fine to include it (chopped).

For other things (raw, where a crunch will be out of place), I only use the very tender parts of the stem with the leaves. Or if the leaves will be more visible as a garnish or accent,  I might strip the leaves from the stems more carefully and not use any (or much) stem. 

This is generally how I treat most herbs that don't have a woody stem,  at least,  if the stem has a nice flavor like the leaves.