Is it ok to store open cans in the fridge?

Short answer: storing food in an open can is normally safe for a short period, but inadvisable.

Longer answer: There are three main issues with storing foods in an open can. They are metal oxidation, contamination, and funk.

1. Oxidation. As commenters have observed, cans used to be made of tin, which is toxic. Modern cans are made from either steel or aluminum. If the contents of the can are acidic, cans are lined with a polymer (plastic) inner layer. If that layer is broken -- say, by a major dent in the can or by using a knife to scrape out contents -- then the acid can get to the metal and, over time, corrode it, and some of the now-oxidized metal will dissolve into the food. As far as we know, the oxidized metal is not toxic, but it tastes horrible.

2. Contamination. Any open container of food can become contaminated when an airborne water droplet (tiny -- microns wide) containing a nasty microbe drips or settles into it. The major biological culprit here is Listeria, which can grow in any moist environment, including spaces refrigerated below 40F (5C). Also, if juices from your raw meat drips onto an upper shelf, which later gets wiped inadvertently into your container of ready-to-eat food, you are likely to get Salmonella or E coli. This risk can be mitigated if you keep your raw meats on the lowest shelf, but not eliminated. Also, it is worth noting that contamination through this pathway is a relatively rare event -- but even so, it is not worth the risk.

3. Funk. Have you ever put an ice cube in your beverage and notice your beverage tastes strange? The chemical compounds that give food their flavor tend to be volatile (meaning they will readily leave the food into the surrounding air). Also, the mustiness of a refrigerator/freezer is due to volatile compounds produced by mold and mildew. Foods that are wet and/or fatty can be molecular velcro to these compounds.

For short periods, cover the can with a plastic sandwich bag and secure with a rubber band. Keeps air out and moisture in.

Newer side edge cut can openers make a lid for resealing the can for fridge storage, so I do it from time to time. I think its an old wives tale at this point, as said people were more concerned with the bpa in the plastic liner than anything else.

I've been told that lead or tin, used to solder/seal the side seam of a can, would oxidize when exposed to air and lead to (mild) lead poisoning. But cans are no longer sealed with lead these days, so: an old tale but not an old wives tale....

The refrigeration system/components will prematurely fail due continued exposure to acidic "vapors" released into the closed environment. Every appliance tech is well aware of the correlation of messy food storage and higher system problems.

I've been storing food in opened cans in the refrigerator for years, and have never had a problem, other than mold, which will occur over weeks in the fridge. I think people are over worrying over this question. As long as it works for me, I will do so. I do use plastic lids if it's to be stored more than a couple of days.

I was taught that keeping opened canned food in the fridge leads to botulism.