I'm going to say the Charadriiformes because they are what first came to mind. The 'shorebirds' are such a fascinating and diverse group of birds, with many different forms, and certain especially amazing members. Part of it might also be that I'm in Central Illinois, away from any major bodies of water, so after I picked up birding I was quite surprised to find that Charadriiformes are actually quite common at certain spots at certain times throughout the country, regardless of proximity to major lakes or the ocean.
Avocets, Pharalopes, and Stilts are amazing animals. The plovers (Especially semipalmated) are adorable, as are Sanderlings and the other Peeps. The Terns are fascinating and very fun to watch dive into the water for fish, and Gulls are nice when I can find the ones that aren't Ring-billed or a Herring.
I suppose Caprimulgiformes, Piciformes, Podicipediformes, Psittaciformes, and Gaviiformes would all be honorable mentions as well.