I do it all the time. Depending on the roads where I plan to fish, I either use my fully-restored, and absolutely beautiful 1982 Schwinn Sidewinder MTB, or my 1994 Specialized Crossroads Hybrid Bike. I have an Instep Trailer that easily holds all my gear, including my inflatable Sevylor Rio Kayak.
I also have an All Rite handlebar rack that holds my rifle, shotgun, or bows and arrows (I use my bikes for hunting and trapping as well...). I am sure it would hold rods also, with no trouble. Here is my Cannondale MTB with the All Rite rack mounted:
Here is my Crossroads rig with the trailer:
And here is my wonderful Sevylor Rio:
If you plan on using your bike for utility or transportation, a trailer makes life a lot easier. There is not much you can't do with a bicycle. I even haul trash, firewood and groceries on mine. With gas prices like they are, I don't understand why more people are not using bicycles.