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The main thing is to realise that these words are different, and actually have different meanings. And a couple of the 'no space' versions aren't actually correct words at all.
As a general rule, when the word "ever" is used to heighten the meaning of how (how ever), what (what ever), when (when ever), where (where ever) or why (why ever), there should be a space between the two words.
ALOT — this is not a word at all!
A LOT — the correct usage, indicating "a large amount of something" (I like this cake a lot!). I've written more about the usage of these words in this article.
ANYONE — a pronoun meaning "any person"(Teasing ducks is so easy, anyone can do it).
ANY ONE — means "any single person or thing". Writing them as two words stresses their singularity (Any one of us could have made the same mistake).
ANYWAY — an adverb used "to agree with a point just mentioned" (I never liked her much, anyway).
ANY WAY — this phrase refers to "some manner of doing something" (Is there any way out of this mess?)
ALRIGHT — just to trip you up - this one is listed as a variant spelling of ALL RIGHT by the Oxford Dictionary, but is thought by most people to be an incorrect spelling, so it's best to stick with ALL RIGHT ...
ALL RIGHT — an adjective meaning "satisfactory, but not great" (The dinner was all right, but nothing to write home about).
ALTOGETHER — an adverb meaning "totally, utterly" (There are altogether too many squirrels around here).
ALL TOGETHER — a phrase meaning "all at once", or "all in a single place" (My lollies are stored all together in one bathtub).
ALREADY — an adverb meaning "before now", or "by now" (I have already eaten all the Easter eggs).
ALL READY — a phrase meaning "everything is prepared" or "completed" (We're all ready to leave for the beach).
AWHILE — an adverb meaning "for a short time" (Sit with me awhile).
A WHILE — a phrase meaning "a period of time" (It's been quite a while since I saw anything that ridiculous).
EVERYBODY/EVERYONE — pronouns meaning "all people" (Everyone has the right to free sunshine, everybody needs it to survive).
EVERY BODY/EVERY ONE — mean "each body or thing specifically" (Not every body has eleven toes, but some do. Pick up every one of those tea bags, or else there'll be trouble!).
EVERYDAY — an adjective meaning "a daily or ordinary occurrence", or "commonplace" (Washing the dishes is an everyday chore, sadly).
EVERY DAY — this phrase means "each day" (I go for a swim every day).
HOWEVER — an adverb meaning "but, yet " (I saw the squirrels gathering, however they weren't carrying weapons this time) or "regardless, no matter how" (However long it takes, I'll eat all these jelly snakes, I'll get there in the end!).
HOW EVER — an intensified version of "how", used to make a point (How ever did you do that?!). This usage is seen more in British English than in American.
MAYBE — an adverb that means "perhaps, possibly" (Are you going to finish that pie? Maybe. I'm not sure yet)
MAY BE — a phrase meaning expressing "possibility" (I may be late this afternoon).
WHATEVER — a pronoun, adjective, and adverb, meaning "lack of restriction" (Choose whatever cakes you like), "regardless of what" (The chipmunks will still attack, whatever you do), "of any kind" (The camels got no help whatever). Whatsoever is often used in this context, too. It is also used as an exclamation ("You're not going out looking like that, young lady!" ... "Whatever!") .
WHAT EVER — is used for emphasis in questions (What ever will they think of next?!)
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