I'm thinking of switching to something like a Goodyear Wrangler or similar on/off road tire, and going up to 235/75 R15. I think (don't hold me to it) you can go up to 235 without any issues, not sure about any larger. I think megascape runs on 245's but he has a lift on his.
Mud Terrain tires are ok if you use the car for off-roading a lot and you can bear the noise which varies a lot from manufacturer to manufacturer.Also extra care must be taken when driving on paved roads, especially when raining.
As for the size, it depends on a few factors and the best way is to take the car to a good tire shop where they can direct you as to your choices.
If you decide to go ahead, stay away from the BF Goodrich Mud Terrain tire.
Im currently using 245/65/17 BFG Rugged Terrain (AT)(Are not shown in my profile pic), they are great compromise between Off Road and Paved terrain.
I've used them with confidence in my farm with a lot of mud, and in the highway.
With off-road tires there is some discrepancy as to the actual overall size between manufacturers.
It is a very rare occurrence for sizes to be a perfect match.
When one goes for the much bigger tires it is advisable to do some on-the-car checking.
1/Put the two front tires on.
2/Jack up, all the way, the rear end of the car.
3/Start the engine and turn the wheels from end to end seeing if they touch or rub against something.If not the size will be OK for off-roading.
This topic started by an individual requiring about mud terrain tires.
For mud terrain one needs narrower and bigger tires with as much profile as possible.
By bigger in the tires linguo we mean bigger in diameter, ie bigger circumference for the same rims which also gives you a much smaller rotational friction, (extremely useful in rugged terrain).
The calculator that christophera was kind to post indicates very clearly the differences and similarities between tires.
For serious mud business you need a profile of at least 75%.