The 45 boxes, like all of these pictured above, are the most common, and easier to find. It's the LP boxes (pictured below) that are really hard to find, and go up in value as time goes on. They really don't make 'em like this anymore. The box on the left is a true Platter-Pak, which were almost always brightly colored, and/or patterned. The box on the right is literally from RCA Records, and is by far the sturdier of the two. Winnie-the-Pooh of course speaks for itself and comes from the 70's.
Nowadays, Crosley is a popular maker of staunch LP record cases, making transport not only easy, but safe as well. There are plenty of DJ quality vinyl cases out there too, but be prepared to shell out some serious bucks for them. This case holds 30 LP's, perfect for an evening of record playing at a friend's house.
Then if you're super serious about transporting your vinyl, the Odyssey case pictured below is as staunch as it gets and holds up to 200 LP's. It's heavy, but you gotta protect your babies, right? What's nifty about this one is the top is detachable for easy flipping through the stacks and display, if you so choose.
Whichever cases you like to use, they're the perfect way to protect your babies while giving them portability, and they look great just hanging out near your record collection too. Even if you find cases which are not in good enough condition to carry around, get them anyway (if the price is right) to use as decor and actual storage. Keep spinning those little black records!