Most pickling and many canning recipes that call for salt explicity state 'Pickling Salt'. The difference between pickling salt and standard table salt is that pickling salt does not contain anti-caking ingredients.
Anti-caking ingredients found in salt prevent the salt granules from clumping together and or liquifying as easily in moist or humid conditions. That's how your table salt falls freely through the small holes of your salt shaker and bounces off your corn on the cob. Iodine is an anti caking agent, look at your salt package, it will generally state 'iodized salt'. Pickling salt is not iodized, it is pure granulated salt.
If you choose to substitue another type for salt for pickling salt in a given recipe, don't worry you're not going to put the universe out of synch, but your pickles shant be too happy about it. Iodine and other additives in standard table salt will not only effect the flavor of your culinary endeavors but will also have other adverse effects on the final outcome. Iodine will make the pickles or produce darker which is only a minor nuisance when compared to its effect on the brine which will be cloudy and visually unappealing.
The larger more coarse grains that comprise standard table salt do not allways dissolve as freely as fine grained / powdery pickling salt which also has an effect on the ultimate outcome.
In conclusion, it's not a good idea to substitute table salt for pickling salt. You can however use pure sea salt so long as it is Pure Sea Salt with no additives which many brands have.
Kosher salt has also been used on occasion. Allthough pickling and kosher salt weigh roughly the same by volume, kosher salt has thicker coarser grains which allows for more air space between grains which will effect the end result, but not overwhelmingly so. Once again the kosher salt you use should be unadulterated and free of additives.