Our house has a wooden basement that is about 25 years old. Recently, I noticed that two of the supporting wall studs have major cracks in them. One of them runs about half way down the stud and is an inch wide split. The other is a crack that runs horizontally into the stud and then runs downward. I don't know how long they have been like this. Is it possible to repair this, and if so, how?

Show us a picture, never heard of a wooden basement. Sounds like an additional stud should be placed along side and "sistered" to the defective stud. "Sistered" just means lots of nails.