Both of the rules offered so far rely on the "American Rule," i.e., each side pays its own fees, but neither makes any mention of the many, many exceptions in which a party may end up paying for everyone's lawyers simply because they lost.
One category that you mentioned an interest in -- slip-and-fall cases -- will rarely be one of thsoe exceptions, but the rule may vary from state to state.
The other category -- IP cases -- can frequently allow for fee-shifting to a the prevailing party. Federal statutes governing patent (35 U.S. Code § 285), trademark (15 U.S. Code § 1117), and copyright (17 U.S. Code § 505) litigation all allow courts to order the loser to pay the winner's legal fees.
And there are many, many more kinds of cases that permit fee-shifting under varying circumstances, including civil rights (42 U.S. Code § 1988), FOIA (5 U.S. Code § 552(a)(4)(E)), FLSA (29 U.S. Code § 216), EAJA (28 U.S. Code § 2412), and antitrust (15 U.S. Code § 4304).
Keep in mind, though, that this means not only that you could be forced to pay the other side's fees, but that they, too, could be ordered to pay yours. You undoubtedly have less money to spend on lawyers, but there are many firms that handle these cases on contingency to address that disparity.
You could fairly say that this has a chilling effect on litigation, but that is probably the point. The courts want to discourage parties from infringing on each other's patents, they want to discourage flimsy assertions of infringement, and they want to encourage the presuit resolution of these disputes.