The formal rule is that adverbs follow verbs, so that traditionally, "__ suddenly can _" would be considered a fault. There was quite a lengthy discussion following the popularity of the TV series Star Trek because of the opening monologue's wording:
To boldly go where no man has gone
This outraged many language purists who insisted that "to go boldly" is the only permissible form. Even today, many still adhere to the rule. Some editors maintain that there is a matter of logic at work; namely, that a subject can "do" a verb in some way, but that a subject cannot "perform" an adverb. [Edit: To clarify per a comment below, the subject of adverb ordering and logic often arises in discussions of splitting infinitives, which are usually split with adverbs.]
One of the examples given by Henry above is incorrect:
Suddenly Spaghetti can talk.
This is possible only if "suddenly" is set off with a comma, as it is phrasal. Finally, "can suddenly" is idiomatic, i.e., what sounds natural to the native ear because the alveolar 'n' glides smoothly to the sibilant 's.' The reverse is awkward to the palate.