I'm not sure you would have enough distinct formats for 10 events; at most you might have 5 or 6, similar to the UK (and short-lived US) show The Krypton Factor. Here's what I would want to see in a hypothetical all-around tournament...
Quiz--Obviously, J! would be the most popular choice here, but as far as a pure test of knowledge/factual recall goes, the UK's Mastermind is a better fit, especially its use of specialty subjects.
Word Association--again, Pyramid would be the obvious choice, and I would tend to agree. But since this is the ultimate test of agility in all areas, why not make it a mash-up of that and Body Language? Contestants would have to alternate in each category (or even each word) between verbal and physical communication.
Stunt/Physical Activity--Either a full obstacle course a la the aforementioned Krypton Factor, or something more small-scale like Minute To Win It.
Memory--Concentration, obviously, although perhaps one could also adapt Simon instead.
Talent--This would be a bit more nebulous, as it would require subjective judging by a panel, but since this is the ultimate test of everything, we need to include it. I would again take a page from Mastermind and make it two different performances--one that the contestant decides for themselves, the other a randomly-selected event (singing, dancing, magic trick, etc.) that they must practice for a week a la The Big Moment.