I have a small Think Tank bag called a Slim Changer that is the size of a small fanny pack. I carry the 135L in that and carry the 6D with a 35L on a Black Rapid strap or sometimes I just hand carry it with no strap. I can get 90% of what I need done with those two lenses.
If I know that I am shooting an event/sports where my mobility might be limited by seats or a fence/guardrail/wall, I will pack the 35mm in the Slim Changer and mount a 70-200L on camera with BR strap and go.
Three lenses owned. Never left the house with more than two. One in waist pack and one on camera. No hoods. I do have B+W filters on each lens for protection.
Minimum for the day, the trip, or to choose from at home? - it depends
There was another thread on this that explored the ramifications. There is also cost to consider.
minimum minimum is a G1X - least weight for excellent IQ
Beyond that, one is optimizing, so my optimal capture anything but I can still schlep it around kit is:
5D3, 24-105, 35 f2 IS, 100L, 100-400 +1.4x & f8 AF, and G1X with underwater housing. If I can I'll add 5D2 and 17-40. I'm leaving soon for Nepal and Bhutan with strict carry-on restrictions and lots of hiking so I'll have just 5D3, 24-105, 70-200 f4 and 1.4x. My wife will have G1X and I'll bring the housing for the raft trip. See, it depends. Fun to think about though.
When I'm in the mood, I will sometimes go out with just a couple primes; I haven't done that since I replaced my 40D with a 6D - I would do that with my 30/1.4 and 50/1.8, doesn't work as well now as I like the 50mm or wider FL (30mm on crop) for most stuff, but I don't like the focusing on my 50 (too noisy + slow), so I see a decent 35 in my future.
I also occaisionally like to go out with my DSC-RX100 just to see what I can do with a 'pocket' camera.
I don't have a minimalist kit, or an everyday kit.
I take what I want for personal shoots, and that changes for day to day, or outing to outing. I like trying new things, or pulling out lenses that I haven't used for a while to get a new point of view.
For an assignment, it's usually fairly limited, knowing what I need beforehand, or bringing a bit extra "in case".
If pressed, "What is the minimum you take if you didn't know what to expect?", I'd take the 5D2, 24-105 IS and 580 II flash. There's a good reason the body and lens were set up as a kit.
Otherwise, I don't see why it would be considered overkill to bring the 1Ds3 and the 28-300L IS (or 1DX, if I owned one). Yes, it's big and kind of heavy. But I don't need a camera bag or other lenses usually, so that's an advantage. Matched up with a 16-35L and flash, there are very few subjects that kit won't handle with great results.
Okay I'll bite again, a gripped 40D is my body...I usually pick-n-choose...no minimum kit really...when shooting with multiple lenses a 50 f1.4 is usually carried.
A G12 is ALWAYS with me, it's carried in a ThinkTank Retro 10 with some water n snacks. Multi-lens kits are carried in a very old Domke F2 and either a 580II or 430II flash, water n snacks. Each setup has a pocket rocket blower, microfiber clothes and lens cleaner, either a TT CF or SD card holder and a small ringed notepad w/pens.
Outdoor in good light
Flowers n plants, little flyers; bugs...17-40L, 100L, 300 f4L IS, 12/25mm tubes
City/Landscapes, 10-22 and 70-200 f4L IS
Action/Wildlife, 17-40, 70-200 f4L IS, 300 f4L IS, 1.4x III
Indoor or Night
Events/Recitals, 28 f1.8, 50 f1.4, 85 f1.8, sometimes 17-40 and/or 70-200
I've been thinking that if the SL1/100D has as good a sensor as the G1X then a decent minimalist kit, weight wise, would be an SL1, 15-85, 60 macro, and 70-200 f4 IS and maybe a 1.4x. 24 equivalent mm to 450 equivalent mm in under 5 lbs. Ok, the 15-85 isn't as good as the 24-105 on FF but LR cleans it up nicely and it isn't as good as that other EFs f2.8 IS normal zoom but its less expensive, lighter and I already own it. But it has to have better IQ (less noise per ISO) than the 7D or it isn't worth it. The 7D is the best example of why you need FF.
You know, if you want to walk around with an SLR and a 50 mm prime (I prefer 35 mm) thats fine, you'll get some great pics, but if you have to capture whats there and there is something riding on the outcome then you need some versatility. So I agree with Carojo.
grins, who cares! money - 2 bodies, 2 lens, 2 strobes for each (minimun).