30's would be as big as I'd go without a lift or changing the rims. You could probably squeeeze a 31-10.50 under it. Any bigger than that and you will need to lift it and get some wider rims with a smaller backspacing. 33's are when you need to start cutting the bumper and hammering the inside fenderwell.

 

Keep in mind that the bigger the tire, the more you will need to regear. I just went from a 28" tire to a 26.5" tire to get better effective gearing. I was suprised at how much it pepped the Sammi up.

BFGoodrich makes a mud terrain tire in 215/75R15. I was very tempted to get that, but went with a 205/70R15 Geolandar A/T-S all terrain. I was dissapointed to find that Cooper discontinued the Discoverer STT in that size, as it has a very agressive tread, very close to mud focused.

 

...what is the biggest tire I can put on a stock Samurai? I ... want to put a decent set of tires on it. ... what is a good common size that is easy-to-find in an all terrain or mud tire....

The OEM Samurai rim is 5.5" wide. Tire manufacturers specify wider rims for wider tires, for good reasons. If you're going to drive on the road/highway much, you should consider sticking very close to the tire manufacturer's specifications. The BFG TA/KO tire is very popular and available in sizes to fit your rims (it's my tire). Larger tires will require a lift, or fender & wheel-well trimming or both. 215's fit stock wheels and without trimming. At 29", 235's are almost 2" taller and 1&¼" wider than stock, and specify a 6" minimum rim width (I'm using 7" rims, but wider rims are heavier -- a drawback on the highway). A small lift is likely required, although some Samurai owners report not, I remain dubious. Larger tire diameters raise your gearing so you'll need lower gears as well (5th gear is already 8-9% too tall on pre-'88.5 transmissions). There's a chart at Oregon BushHackers, but they're a bit optimistic about what actually does fit. This is a very popular subject with a lot of discussion and opinion. You may have to sort through it to find what meets your needs.

Edit: Wider tires can project past the fender flares. Here in Calif. you can get cited (rarely, but it happens). I'm sticking to 235's (~9.5") to stay inside the flares and avoid complications. My rig spends too much time on the highway. And that way I don't need wheels with negative offset / reduced backspacing. Good wheel info site at: http://www.rsracing.com/tech-wheel.html

 

also think about what application you are using it for. If you just want it for looks then go ahead and put what you want on there, but if you want it to preform in a specific environment then you should keep that in mind when choosing a tire. A good mudding tire is not going to be wide. A good all weather tire is not going to be wide. A good sand tire IS going to be wide. If you're trail riding you don't need a really tall tire, but if you are bogging or rock crawling you want something tall to get your diff and axel as high as you can. Just about any tire or application will benefit from a wider stance. The narrow stock rim keeps the tire tucked in close to the vehicle. The keystone style rims you could flip and give yourself an extra couple inches, the rims that you have on there can not be flipped. Regardless of the tire size, get a rim with very small backspacing to set the tires out a little further. That way you know if you ever upgrade to a wider or taller tire you won't be hitting your springs when you turn.

 

mud tires... personal preference and location
The thinking is a skinny mud tire will dig down to the solid ground and pull you out. But remember you need enough lift and a tall enough tire to reach it.
A wide mud tire will float on top and will make it hard to sink it up to the frame/axle. As long as you can spin them (self cleaning) you will not sink up to the frame/axles. Then again I have found if I don't spin them I keep moving better... ymmv. imho. etc.
Think snowmobile. A wide belt spreads the weight out.
(most of the time when someone gets stuck it's from running too much air imho)
Oh, and the stock rubber is 26" tall, making a 29" tire 3" over all taller. But remember, it only makes the rig set half that taller. Each brand varies... after all, they are measured by guys.
I once had a set of 31's that were taller then a friends set of 32's. Different brand...
And this is NOT measuring from the ground up but from front to back or off the rig. Want a little shorter tire? Air down...

 

yeah snow is similar to soft sand.. you want to stay on top of it, but you want to be able to grip it... can't use paddle tires in the snow

The thing with mud and samurai's, If your in it so deep that you could sink past your axel... your in it too deep. Doesn't matter how fast you can run at it, your zuki won't float... for long. Get the axels up as high as you can with the tall tires for deep mud... or just stay out of mud bogs. Stock samurai motor isn't good for mudding... If you gear it down far enough to pull through it, your wheels won't spin fast enough to keep you above it. The 1.3L engine can be geared to go really slow with a lot of PULL, or just kinda slow with no PULL. Fast isn't part of the equation... not enough power to spin the wheels fast with any torque, especially big wheels bogging through mud.