It seems pretty obvious to store the crayons in the original boxes that they came in. The problem typically with using the original boxes is that after a long time of using them, they tend to fall apart. Prevent this from happening in the first place by reinforcing the edges and corners of the boxes with clear masking tape when you first purchase them.
One of the cheaper, neater and easier solutions for crayon storage is to simply wrap a rubber band around them. In every rubber band bundle, include one of each of the colors so that each has a complete set. Alternatively, if there are a lot of different colors of crayons and it is important that they are easy to retrieve, wrap a rubber band around all of the crayons of the same color.
Keep all of your crayons in a central location by storing them in one of the over the door hangers made for personal accessories and shoes with the clear, plastic pouches. Label each of the pouches with students' names or the color of the crayon inside if you choose to sort them by color.
Coffee cans make great crayon storage since they are sturdy and resealable. Collect cans at the beginning of the school year from the students' parents if you don't have enough on hand. Have enough cans so that there are only a few kids who have to split a can of crayons at a time.
Clear plastic containers work great for crayon storage, especially since there are so many different sizes on the market. Depending on the needs of your classroom, you could have one container per student or just a few bins. One container could be set aside just for broken crayons and those that don't fit into a set.
Small plastic and thick glass condiment jars, like those for jams or olives, make great crayon holders since many of them are just the right height. Depending on what you prefer, you could choose jars a little shorter than the crayons so that the crayons are easy to pull from the jars, or containers a little taller so that the top can screw on.
Paper and plastic cups aren't durable, but they still hold crayons very well, keeping them upright and easy to retrieve. When they start to look dingy, they are inexpensive to replace. Also, if a kid gets food or another substance on them, you don't have to clean them since you can just throw them away.
While the plastic fruit and vegetable baskets from the grocery store that items like tomatoes come in don't have lids, they are the perfect size for crayon storage and they make it easy to pull crayons out and throw them back in at the end of the art project. If you are very concerned about crayons falling out, you could always cover them with plastic wrap held in place with a rubber band.