What is casual Magic? It occurs to me that although this forum exists, that question probably remains unanswered. The variety of decks and discussions that show up here clearly show that there isn't exactly a consensus regarding what defines a casual deck. To parody Mike Flores, casual doesn't mean bad. If you play with bad cards, please don't call them casual.
For some people, casual is embodied by an alternate deck building format. Highlander, Mental Magic, Peasant Magic, and 5-Color are all examples of alternate formats. These formats are what I like to call "competitive casual." The rules regarding deck construction are as strict as those for Vintage or Standard -- they're simply a little bit wackier. The format itself may impose some additional rules as well (ante in 5-Color, all of Mental Magic). Nonetheless, the rules regarding these formats are firm enough that they could serve as the basis for a tournament. Assuming enough people play, a metagame could develop and they'd really just be a microcosm of competetive gameplay. Vintage players in particular can respect this notion, since the stakes of Vintage tournaments seldom yield the same sort of fierce, amoral competition that one sees in professional competition. If alternate formats are "competitive casual," Vintage is "casual competitive."
Another form of casual that arises is multiplayer casual. Two-Headed Giant, Emperor, and Limited Infinity are good examples of casual, multiplayer formats. Decks may be constructed according to any deck building format -- sanctioned or casual alike. The casual nature of the game comes not from the cards being played, but from the way in which the players interact. Because these formats tend to emphasize having fun in a group, I think of them as being more casual than the "competitive casual" formats described above.
There is another form of casual deck building, however, that neither of these categories encompasses. That form is "casual Vintage," as Ecko (from #themanadrain) so aptly called it. It's the format of many non-competetive players -- build decks out of whatever cards you can get your hands on. That's not a bad idea, but it makes for poor discussion. Assume for a moment that a player has an infinite pool of cards. As far as I'm concerned, this describes most Vintage players anyhow. What, then, differentiates a casual Vintage deck from a competitive one? The answer is, "the player." Although few say so outright, most casual deck builders design their decks with any number of constraints in mind.
For example, consider my recent creation,
Hitchcock's "The Birds." My constraints in building this deck are clear: The deck must utilize Faces of the Past, the creature type I wish to use is "Bird," and the deck must utilize Keeper of the Nine Gales. Not explicitly stated, but obvious (if you know me) is that this deck will not include random Power 9 cards, if only because I don't have them. In keeping with these constraints, for example, I turned down a suggestion that I use Battle Screech. I'd have to remove Zephyr Falcon and/or Bay Falcon to make room for more white creatures. That would draw the emphasis of the deck away from Keeper of the Nine Gales, so I discarded the idea.
Obviously, it isn't necessary to think about the constraints of your deck every time you set out to build something casual. Sometimes, the deck really will be "the stuff in my box of cards that looked like it would work well together." For the purposes of discussion, though, it is helpful to have constraints in mind and to state them explicitly. After all, if you don't state the boundaries within which you're operating, there's no reason why your casual control deck shouldn't inevitably drift in the direction of a Slaver variant. On the other hand, if you state, "I want it to use Mystic Snake and Argothian Wurm, but avoid Survival of the Fittest and Oath of Druids," then you have a set of constraints that can define a new direction for the deck. Rather than just vaguely telling people who suggest new cards "that doesn't really fit with what I want the deck to do," be ready and able to explain just
what it is the deck wants to do and
why their suggestion doesn't fit with that plan.
Also, keep in mind that TMD has a fantastic community with a lot of expertise. If you want relevant commentary on your deck, however, it is helpful if you treat your casual creations with the same dignity as you would treat a competitive deck. Comment on your deck at length, explain any card choices that may seem unusual, and be open to criticism. If you obey the TMD forum rules with your casual decks, your readers will be encouraged to write helpful comments. Bare deck lists are no better for casual commentators than they are for competitive ones.