Lawsuits happen because two (or more) parties can't agree on something.  In the cases presented below the disagreement was with Farmers Insurance Group's handling of claims or business practices.  If you have references you would be willing to add I would like to hear from you!

http://www.publications.ojd.state.or.us/S47182.htm: Olivia Erickson v. Farmers Insurance Company of Oregon (claims dispute) Supreme court of Oregon (CC 97C-12315; CA A103338; SC S47182)
In this case the plaintiff was denied complete coverage by Farmers Insurance, regarding an accident involving an uninsured motorist.  The total damages was deemed to be $140K but the policy limits were $100K.  The catch?  The plaintiff had two identical policies (his and his wife's)  both were in the car, so both policies should have been accessible for coverage.  Farmers said no-way, but the Oregon Supreme Court system disagreed and the plaintiff was awarded the monies.
http://www.kscourts.org/ca10/cases/2005/12/03-3234.htm Judith A Bryant v Farmers Insurance Exchange (age and gender discrimination) No. 03-3234
The Tenth Circuit Court of appeals finds that the lower court inappropriately ruled on the age discrimination case brought by the plaintiff (and appellant).  Furthermore the court found that the low ratings the plaintiff received were, in fact, caused by the person who replaced her, and who admitted the he was sent to the office to take her job!  Way to go Farmers.
http://www.kscourts.org/ca10/cases/1997/12/96-5197.htm Abed Damaj v. Farmers Insurance Company (claims dispute, low balling, bad faith) Case N0: 96-5197
The Tenth Circuit Court of appeals finds that the lower court inappropriately ruled and that Farmers Insurance acted in bad faith, specifically by suggesting a price/value for a stolen car before asking for a quote from area dealers.
In particular:
Stephens specifically criticized Farmers' practice of obtaining price quotes for stolen vehicles from used car dealers by suggesting a price range to the dealers and asking if such figures sound about right: "Farmers failed to perform a fair valuation of the plaintiff's van because of its failure to follow accepted valuation practices by reliance on independent and verifiable written sources of information."
http://www.madisonrecord.com/news/newsview.asp?c=184071 Not a court record, but still interesting :-)
Low balling a homeowner who lost their house to a tornado to the tune of $400,000!  Dear me.
http://www.court.state.nd.us/court/opinions/20020209.htm Daniel Wilson v. Farmers Insurance Group.  Supreme Court of North Dakota, Case No: 20020209
Wilson appealed a lower court ruling in favor of Farmers Insurance.  The initial claim was for parts stolen off his Ranchero.  Farmers ultimately denied the claim, not because it was without merit, but because in Farmers opinion, Wilson had not cooperated enough. 
Here's what the judge said on the matter:
In the present case, a question of fact exists as to whether Wilson substantially cooperated with Farmers Insurance. While it appears from the record Wilson did not happily jump through the hoops of the investigation, a review of the evidence, in a light most favorable to Wilson, shows he attempted to cooperate, to an extent. He sat for a recorded statement with a Farmers Insurance special claims representative, but the representative's tape recorder malfunctioned. Although he walked out of an initial session because of its long length and his frustration with the examiner, Wilson did complete an examination under oath as required. During its investigation, Farmers Insurance repeatedly requested tax returns, Social Security records, and other financial records. The record shows Wilson provided an explanation regarding the tax returns, provided the Social Security records, and provided some financial records. While Wilson may not have been fully cooperative with Farmers Insurance and Farmers Insurance may not have been satisfied with the contents of Wilson's records, we cannot say, as a matter of law, that he has not substantially complied with the cooperation clause.
FarCry - Mollio