Find the most iridium

1. Geodes - there were threads all over claiming their contents was impacted by luck. However Tallian linked this thread on reddit in the comments that suggested otherwise. The OP could be better worded, so I'll restate. What you get out of Geode's appears to be deterministic. I did a very small test last night and opened a couple of geodes, force closed the game, and then opened them again. I got the same set of things in the same order both times. So it appears Geode content is set in some manner. It also might be true that it's deterministic by type, as per this comment in the thread (essentially, that the type of geode + the "nth Geode opened" is what determines the drop). Unfortunately I only had basic Geodes on hand for my test. There have been arguments that what a Geode contains is set when the Geode drops. However nobody has found evidence in the save files, which contain lots of information about the things your character possess. So I would say Geode contents are not affected, but Geode drop rate probably is.

2. Drops in the Journey of the Prairie King arcade game in the Saloon. I haven't played the other game but if it has drops then it affects those as well.

3. What you find in the mines. A good fortune means you are more likely to find a stair under a rock. I believe it impacts the spawn rate of rocks with ore/minerals in them as well.

4. Fishing.

Obviously a bad fortune works against you while a good fortune works for you.

Crops @JohnDubya says he has read that fortune impacts crops. I can't offer much in the way of evidence on this one, but here goes. I've put something like 14+ seasons of crop growing into this game (less a couple of winters without the greenhouse) and as I tend to harvest as soon as possible and use quality fertilizers I can't speak much to whether luck might be impacting harvesting. In my current game's green house, I only use speed growth fertilizers (I'm increasing my base for star, ancient, and rare seeds). I pulled two ancient fruit the other day and got a silver and a gold despite it being a worst-luck day. I almost always get some quality out of the crops there and I know I have harvested on a series of bad luck days over the past in-game month (as I'm just building up a seed base I don't have any steady crop rotations; most times I harvest in batches of 2-6 plants). In my very humble opinion, waiting for a "good luck" day to harvest is a bad idea even if it impacts the quality of what you harvest unless one is well into the game and has a terrific economic base. Plant with Quality Fertilizer instead and there will be plenty of gold starred crops.

Of the five legendary fish, the Angler and the Mutated Carp are definitely the easiest to catch and with good practice won't require any special equipment other than an Iridium pole and basic bait.

The Glacierfish and Crimsonfish are much more difficult to catch due to how quickly they will jerk from the top to bottom of the scale. I have yet to catch the Legend; however, I was met with success in catching the other 4 by doing the following:

1) Craft premium bait (recipe obtained from Linus). The premium bait seemed to attract the legendary fish more frequently, which saves time spent attempting to catch them.

2) Purchase or craft a few Cork Bobbers and Trap Bobbers. The Cork Bobber (750g or 10 wood, 5 hardwood, 10 slime) expands the fishing bar. The Trap Bobber (500g or 1 copper bar, 10 sap) slows down how quickly the fish escape while not being reeled in. The bobbers will degrade, and having 2 of each will allow you to do a full day of fishing with no problem.

3) If your fishing level is not already 10, purchase or prepare skill boosting meals! The following meals will help you boost up your skill to 10, which expands your fishing bar as well.

Trout Soup : Fishing +1*
Chowder : Fishing +1
Escargot : Fishing +2
Fish Taco : Fishing +2
Dish O' The Sea : Fishing +3
Fish Stew : Fishing +3 Lobster Bisque : Fishing +3

*: Trout Soup is only 250G per meal from Willy's shop, so consider this an easy meal to bump from 9 to 10 if you're about to lose out on the season.

4) Keep trying and don't give up! If you're really tight on time, find a day with the perfect conditions (no crops to tend to or other responsibilities), and at the worst you can always 'Quit to Desktop' before the day is over to give it another day's attempts.

Other Advice:
For fish that like to jerk around in the water, always try to just barely have them caught. That way, when they dive up or down, you can react much more quickly and don't have to move as far.

DO NOT attempt to use the Barbed Hook on the Crimsonfish, Glacierfish, or Legend. You'll be spinning your wheels with how sporadically the fishing bar will 'adjust' -- (sway wildly).