Plan ahead, because marshmallow-making takes two days -- don't worry; most of that time is waiting, not working. First, soften the gelatin and make the sugary syrup.
Sprinkle 2.5 tablespoons of unflavored gelatin into half a cup of cold water (this is important because cold water dissolves gelatin best) in a mixer bowl and leave it alone while it softens. Remember: One packet of powdered gelatin is about 2.5 teaspoons, and there are 7.5 teaspoons in 2.5 tablespoons, so you'll need 3 packets in this gelatin-to-water ratio (always best to measure, though).
While the gelatin dissolves, make your syrup -- although this is mostly just sugar, this is where the flavor (and color) happens. Combine half a cup of water with sugar (1 cup corn syrup and 1.5 cups of granulated sugar) and a pinch of salt (just a quarter teaspoon) in a medium (2-quart) saucepan. Stir the mixture over low-to-medium heat until the sugar dissolves; then boil, without stirring, until the mixture reaches 240 degrees Fahrenheit (115.6 Celsius) on a candy thermometer.
When it comes up to the correct temperature, remove the syrup from the heat and slowly pour it into the gelatin, beating the mixture on low speed as you pour. Once you've added all the syrup, beat the mixture on high until it thickens, which should take about 15 to 30 minutes (it will also grow as much as triple in volume, so use a big bowl).
To make flavorful marshmallows, add a teaspoon of flavor extract such as vanilla or peppermint, or root beer, lemon oil, or espresso to the batter before pouring it out into a baking dish. To make colorful marshmallows, add a few drops of food coloring to the batter, again before pouring it into a baking dish (or skip the dyes and add seedless fruit jam to the syrup mixture before combining it with the gelatin). When adding flavoring or coloring to the gelatin mixture, add them in the final 60 seconds of high-speed beating to be sure it's well incorporated.
Pour the mixture into a lightly-oiled 9 by 13-inch (22.9 by 33-centimeter) pan. Make thinner or thicker marshmallows by using a larger or smaller pan, and make things more interesting by sprinkling toasted coconut, melted chocolate, or powdered sugar into the pan before adding the batter.
Cover loosely -- this is the when the wait begins. Allow the marshmallows to set at room temperature overnight (the gelatin really needs at least 8 hours to set properly, if you can wait). Turn the marshmallows out onto a cutting board, cut with a sharp knife (a pizza cutter will make this quick work), and store leftovers for about 2 to 3 weeks in an airtight container.