What Crazy Bridge Bidding Systems Actually Work In Practice?
Always Play The Nine

The great and not a little anarchic British player Zia Mahmood - and correct me if any of this is wrong, as I'm recounting it from hazy memories - was once saddled with a partner who wasn't the greatest.  After trying and failing to get her to understand the basics of leads and so forth, he finally gave up, and invented a new system.  If she had a nine, she should always play it.  Apparently a middle-of-the-pack lead like this was much less likely to instantly compromise the contract than various of the other options.  Zia's partner was pretty happy to have so many fewer confusing options to deal with, and apparently they were able to do a lot better at the Bridge table for the rest of the evening!

Strong Pass System

I can't claim to be as interesting and funny as Zia Mahmood, but once, a slightly insane friend of mine and I cooked up a strong pass system and played it online.  Sitting in first seat, a pass meant a huge whack of points and was incredibly forcing... all other bids were an increasingly elaborate attempt to build on that.  Yes, it would have all fallen apart if we'd told our hapless opponents what we were playing, but as a one-off joke it was wonderful.  Our crowning glory was managing to go down just a couple of tricks undoubled against a partnership who had 30 points between them - in first and third seats our repeated aggressive bidding (signifying of course that we had nothing at all) completely impeded any ability they had to take control of the bidding, and then their defence was deeply confused by the fact they thought we had completely different hands to the actual truth, at every turn!  I still feel a bit guilty that at the end of that game our opponents congratulated us for some of the most amazing play they'd ever seen at the Bridge table... we were being so naughty, and they were so nice!