What are the type elements vulnerabilities?

This changed in early 2017; Pokémon Go introduced immunity (basically as double resistance, 0.51x) and modified the Super Effective / Not Very Effective (to 1.4x / 0.71x) as well.

This is nicely displayed, as well as discussed, in this reddit thread. The image from that thread follows.

There are a lot of elements, so I'm just going to link to this table which summarises them all for Pokemon X & Y; I expect the list for Pokemon Go may be slightly different, but I don't think anyone has yet compiled a table for that.

For example, water is super effective against fire, fire is super effective against grass, and grass is super effective against water.

And here is an alternative representation of the same information that may be easier to read for some. The center column is the attacking type; it is super effective against the types to its right, and not very effective against the types to its left.

Another representation of types that may come in handy:

The Table Attack \ Defense Table

• Below shows which Pokemon Attacks are strong
• Attack on Left, Defending/Pokemon Type along the top
• 1.25 means they deal extra damage, while 0.8 means they deal less damage

Visual Table as Image

Here is the solid reference to Google Doc by TheSilphRoad on reddit, where it was determined by actual game play stats.