Fishing is one of my main destinations for touring trips. I grew up fly-fishing but have recently gotten more into spin fishing, which can occasionally be easier on slow water in the middle to south parts of my state.
My main touring rod (like cyccommute) is a light weight 8ft 5wt 5-piece fly rod from Cabela's. That one goes on every trip just in case I stumble upon a nice spot. And Cabela's has a great replacement warranty since I'm really hard on my gear. I'll carry one of my nice travel rods -- Winston or Gray's -- if I'm going out specifically to fish. Reel is usually a nice Bauer that has seen a lot of abuse.
My touring pack always includes: annual license; 2-3 9' 4x leaders; spools of 3x, 4x, & 5x tippet; hemostats, water thermometer, floatant gel, or some other little pieces of misc gear. I also carry a 5 oz birding monocular that helps me spot potentially fishy sites across a lake and is fun for watching birds or wildlife in the area.
My fly box always includes: Hare's Ear soft hackles, Muskrat soft hackles, Pheasant Tail nymphs, Elk Hair Caddis, foam ants, black Wooly Boogers, San Juan worms, Y2K bugs, Bream Busters, and some generic dear-hair bass bugs. I'll usually pick up some local flies, but this assortment gets me through 90% of my fishing situations for trout, bream, bass, and crappie.
The small fishing bag (flies, leader, misc) weighs maybe 6-7 oz. The rod, reel, and case are about a pound and a half but I haven't weighed them. I'll carry a pair of sandals during the summer time for wading.
My small spinning rod and reel are about the same but I don't have a good lure box yet, still learning about that stuff. If anything I'll carry a small jar of PowerBait which works but doesn't feel good to me.
An even easier fishing set up would be a long but light-weight fly blank built with minimum guides, no reel seat, and a small handle. You could use it as a "pole" with found worms or bugs or whatnot. But flies are so versatile, fun, and light-weight that I won't travel without them.
The other guys are right on -- gut and clean the fish, wrap in foil, smother in coals from a campfire. Garnish with whatever's available and serve with whatever else you have. It's hard to go wrong with fresh fish in the out of doors.