First you have to figure out what cans are made of. There's many metals used, and then there's alloys of those metals.
Tin (or rather tin plated steel alloy), and aluminium seem the most common. http://en.wikipedia.org/wiki/Tin_can
Wikipedia has this to say about tin poisoning from cans:
Tin has no known natural biological role in living organisms. It is not easily absorbed by animals and humans. The low toxicity is relevant to the widespread use of tin in dinnerware and canned food. Nausea, vomiting and diarrhea have been reported after ingesting canned food containing 200 mg/kg of tin. This observation led, for example, the Food Standards Agency in the UK to propose upper limits of 200 mg/kg. A study showed that 99.5% of the controlled food cans contain tin in an amount below that level.
For aluminium, toxicity is even less apparently:
Despite its natural abundance, aluminium has no known function in biology. It is remarkably nontoxic, aluminium sulfate having an LD50 of 6207 mg/kg (oral, mouse), which corresponds to 500 grams for a 80 kg person. The extremely low acute toxicity notwithstanding, the health effects of aluminium are of interest in view of the widespread occurrence of the element in the environment and in commerce.
Thus, it's highly unlikely you'll suffer any ill effects from food exposed to the metal of your can.
In the past lead solder was used to seal the cans, which did lead to poisoning as lead of course is rather toxic (which was not well understood at the time):
Early cans were sealed with lead soldering, which led to lead poisoning. Famously, in the 1845 Arctic expedition of Sir John Franklin, crew members suffered from severe lead poisoning thought to be caused by eating canned food. More recent research suggests the lead poisoning was more likely to have been caused by the internal pipe system on the ships.
This could well be the origin of this myth, however the poisoning could happen with sealed as well as opened cans.
Now, with the scare about BPA poisoning, the internal coating/liner of modern cans is blamed by some for all kinds of scary diseases as well, but as mentioned in other questions there is no real scientific evidence to back up the claims that BPA is toxic in the concentrations found in those linings except maybe for infants.
For example a recent US government study indicates that:
- For infants and children the Expert Panel has the following levels of concern for biological processes that might be altered by Bisphenol A, as follows:
• some concern for neural and behavioral effects
• minimal concern for the effect of accelerated puberty
- For adults, the Expert Panel has negligible concern for adverse reproductive effects following exposures in the general population to Bisphenol A. For highly exposed subgroups, such as occupationally exposed populations, the level of concern is elevated to minimal.:382-383
Ergo, I can only conclude that there is no reason to assume that having open cans in the fridge as storage containers would cause any adverse effects on your health, as long as the same precautions are taken as with any other food container. Any effects that might ensue would be no different from having the sealed can in there.