I heard something about a god-damned departure tax payable when you leave Mexico by land, or payable at a bank beforehand or something daft like that. I have searched but I cannot find anything definitive about thes. I have got the 180-day tourist card, and I thought all I need to do is turn in that and get an exit stamp in my passport. Can someone please clarify?

You really don't need to do anything at all. Many don't turn in their FMT. It is a good practice and they'll take it but there is no exit stamp or tax. If you have brought a vehicle you'll want to turn in your sticker and get a receipt and keep it.
There is no exit tax, but there is a tourist tax for your FMT, about US$20, that you can pay at a bank. You should do this right away to avoid trouble down the road.

And just why is it such a big deal to pay the "god-damned departure tax" anyway? You are visiting another country and supposedly enjoying what that country has to offer, why should they let you do it for free? Many countries charge a departure tax. How about the $95+ the US government charges in taxes to fly to Mexico?

What one hears+ is not always accurate. The payment for the tourist card - a form of visa fee - covers all fees due the Mexican government for individuals when entering/exiting by land. I don't know much about fees assessed for vehicles, if any. Actually, that per-person entry fee is low, judging by what I've paid in other countries (more than US$100 for entry into Brazil (and the other way around for Brazilians, too). Additional taxes, fees and/or surcharges are assessed by airlines, airports, security and taxing bodies, etc., when making a trip into Mexico by air. The United States government +does not+ charge "$95" in taxes on tickets for flights to Mexico - as asserted in #3.

Surely if this guy's got his "180 day tourist card" he doesn't need to go to a bank or pay any more? No exit stamp required - just leave (as #1 said in the first place).
#5, if he came by land (implied in his question), he does have to pay. The cost of the FMT is included in the price of a plane ticket, but when entering by land or sea, one must pay at a bank. Some, but not all, immigration modules at the border have an adjacent bank window where the FMT can be paid.

Here's my understanding of the fees if arriving by plane:
On the plane, you should be issued with a form called Forma Migratoria Para Turista, Transmigrante, Visitante Personade Negocios o Visitante Consejero – Internacion Aerea (in English: Migratory Form for Foreign Tourist, Transmigrant, Business Visitor or Councilor Visitor – Entrance by Air). Fill it out on the plane before presenting it to immigration on arrival. Immigration will keep the top part of the form and you keep the bottom part with your passport. The fee for the form is usually included in the cost of the airline ticket, so nothing to pay on arrival in Mexico and nothing to pay at a bank. The FMT allows a maximum stay of 180 days and the immigration officer will write in the actual number of days you can stay; it will be between 30 and 180 days depending on your nationality. If you don’t get a form on the plane, ask some questions (or ask your ticket issuer when you buy your ticket).
If you arrive by land, you will get a similar form but you will have to pay the fee at a bank before you depart Mexico.
This is what happens when you leave Mexico and go to Belize...
When you cross the border to Belize, you have to report to a small immigration booth on the Mexican side of the border. They will ask you (in Spanish) for MXP100. If you pay, you keep the FMT which will allow you to re-enter Mexico within the allotted time (30 to 180 days) without paying a new re-entry fee.
You may choose not to pay the MXP100, but you hand over your part of the form and the next time you enter Mexico, you will have to pay a higher fee (it's something like MXP280) for a new FMT. And that fee isn't paid at the border, but at a bank.
So relax, no departure tax. You already paid to get in!

I believe some posters have said the Mex. government is now insisting that the FMT fee be paid before leaving the border area, that is, the 15 or 50 km area near the border. So, when one receives the FMT if it is possible to do so, pay ASAP, don't wait until you go back. Some folks do enter at small centers which do not have a bank anywhere near; others may enter when the banks are closed.
It is not at all a departure tax. It is the fee for the FMT, and allegedly is intended to be used for tourist enhancement purposes. Hee, hee.

$20 is a bargain for entering Mexico. The US charges Mexican applicants for a tourist visa $130 USD just to apply, no refunds if denied. Then they state plainly that possession of a visa does NOT guarantee admittance; that is up to the immigration people at the port of entry. So you can travel hundreds of miles to a consulate., pay $130, buy a plane ticket, and still get turned back at the border.