Define offroad use...
You're not going to be tackling the Rubicon in a stock Subaru..or even a mildly built one for that matter. Subaru's are designed with one of the best AWD systems out there geared towards snowy roads. With that said the best "offroad system" Subaru offers is on the STi with a manually controlled center differential and front and rear Torsen LSD's. However not many outfit a 300 hp rocket to be used on unimproved roads, its been done, but not by many. I personally have a 2006 Impreza 2.5i that i absolutely love. I can get 35mpg on the hwy with a light foot and keeping it around 65mph. That drops to around 28 in the city. I have also drove this car several miles up Corova Beach in the OBX despite the recommendations from those with Ladder frame 4x4's. Not once did I get stuck, but I did scrape a good bit along the way. From the factory my car has 5.6" of clearance. Outbacks and Foresters have around +/- 8.7" which I imagine would help with the belly scraping. The 5 speeds offer close to a 50/50 split in most conditions as the center differential is a viscous coupling unit. The Automatics use a 4EAT 4 speed transmission that sends 90% of the traction up front and 10% to the rear, with the ability to split it to around 55F/45R. There is a modification that's been done to trick the tranny into sending power 50/50 much like a center diff locker.
Again, it depends on your definition of offroad but you have to keep in mind that despite the modifications you make to these cars, it's still a car with CV axles and a light duty body and powertrain. Although it's been done many a time I would not take my DD up and down Jeep trails on the regular. I have plans of adding Forester XT springs and struts to my car which will yield a 2" lift, and allow me to fit 215/65/R16 tires. All said and done I will have close to the ground clearance of a stock Forester or Outback, if not a bit more. As it sits now, this car is a champ in the snow, and its lightweight makes it awesome in sand (with revs kept a bit higher). I've taken it up and down many forest roads here in NC (that admittedly a Prius can go down) and have never had a problem. As far as modifications go, I would highly recommend a skid plate being the first thing you do, since plastic typically always loses in the fight against rocks and logs..
I hope that helps, and ask away if you have anymore questions.