Not weird, not even all that remarkable in a way, but a catch I will
nevertheless remember forever: I once caught my own sunglasses.
Specifically:

I was travelling the country with a friend during a summer break in
college. I bought a Mickey Mouse rod at the beginning of the trip
(literally - a child's spinning rod, about 2' long), and used that on
the few occasions we tried to fish. For this particular incident, I
was somewhere in Yosemite park, standing in the middle of a fast
moving river past my waist. I was mildly hallucinating, though
whether from very good weed or something stronger I don't recall. I
do recall it was a nice, sunny day, and, given my various handicaps, I
had zero hope or concern for actually catch a fish. I was happy just
throwing the lure out, using my specially-developed lasso-style cast
(imagine a stiff two foot rod, holding it directly overhead, twirling
it something like a lasso, and then releasing at the correct moment to
shoot the lure in the desired direction.) Not sure how it happened,
but I dropped my sun glasses. They immediately washed away and
disappeared, not a hope in the world of finding them again, short of
emptying out the river and searching amongst the myriad of golfball-
sized, multicolored stones for hours on end. A couple of real
fisherman were watching from the shore, along with my college friend,
who was also hallucinating and thus thought my losing the glasses was
hilarious. The humor was not lost on me, in this case aided by my
handicaps, especially helpful in that these were prescription
sunglasses which would have cost about a months worth of road living
to replace, which would not have been an option in any case, and so
I'd be driving the remaining 5,000-odd miles with a potentially deadly
handicap... but... I kind of thought... that maybe about 40-50 feet
away, in about 4 feet of rapidly moving water, on the bottom of the
river downstream of me, amongst the millions of golfball sized rocks,
I saw a brown something that looked vaguely like something. I was
absolutely certain I was seeing things, just looking at a rock, but I
didn't let on. I told my friend and the real fishermen who were now
observing at this point, "Watch." I calmly spun my Mickey Mouse rod,
cast 40' downstream, worked the line until the lure sank to the bottom
- difficult in the current - reeled carefully, slowly, deliberately...
thought maybe possibly I felt some extra weight against my line...
30', 20', 10'... the observers on shore sure I was full of ****, as
sure as I was... the pace slowing and tension mounting as I got to 5',
3', 2'... me growing increasingly certain that I must be seriously
hallucinating, cause it sure looked like there was something on the
end of my line... kept reeling... and pulled my sunglasses from the
water. They slipped off the lure as I reached out my hand -- they'd
been just barely balanced against the tip of the lure -- put the
glasses back on, and resumed "fishing." To applause from shore. (The
fisherman. My friend had collapsed and convulsed in disbelief at this
point, not to return to his feet for a good twenty minutes.)

A stupid story, but one I remember well.