Yes, when you control Guile and counter a spell, you can cast that spell immediately, no matter what type it is.
To explain, I'll need to give a little background. The Magic rules are fundamentally constructive in nature: they define all of the parts of the game and procedures, then list the things you are allowed to do, and then subtract the things you are not allowed to do (not necessarily written in that order). For example, there are rules that define your hand and battlefield, and cards, and permanents, and the land type. Then there is a rule that says when you are allowed to play a land, and what restrictions there are on taking that action.
Now, if we consider the rules regarding the Creature type, we see that rule 302.1 says
A player who has priority may cast a creature card from his or her hand during a main phase of his or her turn when the stack is empty. Casting a creature as a spell uses the stack. (See rule 601, "Casting Spells.")
It does not say that you are not allowed to cast it at other times. If something else does allow you to cast a creature spell at another time, there's nothing stopping you from doing so. Now, the third step of resolving a spell or ability, 608.2c, says
The controller of the spell or ability follows its instructions in the order written. However, replacement effects may modify these actions.
So when you control Guile and counter a Creature spell, Guile's replacement effect modifies the counterspell's instructions to say that you exile the spell and you may cast it. Now you have another instruction giving you an option to cast a (particular) creature spell, in addition to the option provided by rule 302.1.
The timing rules for other types is worded similarly to 302.1, so this same logic applies to other types.