PostgreSQL equivalent of MySQL memory tables?

No, at the moment they don't exist in PostgreSQL. If you truly need a memory table you can create a RAM disk, add a tablespace for it, and create tables on it.

If you only need the temporary table that is visible between different sessions, you can use an UNLOGGED table. These are not true memory tables but they'll behave surprisingly similarly when the table data is significantly smaller than the system RAM.

Global temporary tables would be another option but are not supported in PostgreSQL as of 9.2 (see comments).

Answering a four year old question but since it comes on top of google search results even now.

There is no built in way to cache a full table in memory, but there is an extension that can do this.

In Memory Column Store is a library that acts as a drop in extension and also as a columnar storage and execution engine. You can refer here for the documentation. There is a load function that you can use to load the entire table into memory.

The advantage is the table is stored inside postgres shared_buffers, so when executing a query postgres immediately senses that the pages are in memory and fetches from there.

The downside is that shared_buffers is not really designed to operate in such a way and instabilities might occur (usually it doesn't), but you can probably have this in a secondary cluster/machine with this configuration just to be safe.

All other usual caveats about postgres and shared_buffers still apply.