I must confess that I have never played FATE, but I've heard a lot about it. One thing I never heard was that it was ill-suited for random tables. I guess I never thought about it because I just assumed random tables had nine items ranging from +4 to -4 with 0 being the most common result.
Over at Spirit of the Blank, Mike Olson posts about an RPG.net thread featuring a FATE triangle - a very elegant way to use FUDGE dice for a random table.
The thread on rpg.net features discussion of using this as a slick setting generator. For example, if you have three controlling powers called The Church, The Intelligentsia, and The Free Thinkers, results could show to current balance of power with the most common result that all three groups are about equal.
Another use for it would require several charts featuring two for character generation. Basically, have a chart represent an NPC chart. NPC magic has the attributes INT (mage), WIS (priest), CHA (psionicist). NPC mundane has the attributes STR (Warrior), DEX (rogue) and CON (Warrior). The three corners would have 17 for the primary stat, but weak in the other two. Thus, to generate an NPC, decide if he/she will be magical or mundane. Roll on both charts and you have stats. Other tables would have equipment packs, spell/power lists and the like. With ten tables, you could have a fairly extensive NPC generator.
I had a three-way table that produced possibilities of Psionic, Wizard, and Clerical magic powers in terms of levels. The idea was that in a newly visited world, what forms of 2e magic were present and at what levels. If it was a high-magic world with some clerics and no psionicists, the entry would read wizards to 20th level, clerics to 10th level. Since psionicists weren't mentioned, they wouldn't exist.
Unfortunately, I do not have adobe acrobat installed at home (I use Foxit Reader and SumatraPDF instead) and the table was lost. I can't seem to remember to print the result with a PDF printer instead of save a copy of the PDF results. But those are my personal problems...
I think it makes a new and interesting type of random generator table. What non-FATE use can you come up with?