Walker gets one in the pilot episode. Three guys who raped a young circus performer have come to Walker's ranch—where the girl and her two co-performers are staying for safety—and proceed to chase the girl in an attempt to kidnap her. Walker shows up and, well, ass gets kicked. Then we get this gem from the thugs' leader, with Walker's response:
Leader: You screwed up, Ranger. You forgot to read us our rights!
Walker: You're right. You have the right... (kicks leader in the face, knocking him down) ...to remain silent.
In the Children of Halloween, we see Walker singlehandedly fighting a cult of torch weilding satanists. He goes after the leader, who attempts to stab him, but ends up stabbing himself accidently. The following sort of borders onto Nightmare Fuel when we see (possibly from the Leader's point of view) fire and then we hear laughter.
Any time Walker has to deal with Victor La Rue. Period.
"The Avenger" is a particularly notable episode, because Walker is forced into a series of Vietnam-themed death matches by a fellow 'Nam war veteran, Caleb Hooks, out of vengeance for killing his brother, Randall, in a standoff. These fights are much more creative and intense than the usual fare of beat 'em ups (fighting in total darkness, over Punji stakes with katanas, and inside an electric cage with mechanical torches) and they eventually lead up to a dramatic knifefight with Hooks himself.
Walker's battle with Philippe Brouchard is one of the very few fights in the series where someone is on equal standing with his caliber of skill. It plays out like a genuine fight for one's life instead of the usual Curbstomp Battle, similar to Die Hard in some respects (the bad guy hides his identity and holds a building hostage).