Auxiliary verb and adverb ordering

Ignoring the fact that nobody would suggest that spaghetti can talk, suddenly or not, the phrases

Suddenly spaghetti can talk.

and

Spaghetti suddenly can talk.

mean that there is a sudden change after which spaghetti are able to talk. By contrast the natural meaning of

Spaghetti can talk suddenly.

should mean that spaghetti are able to talk in a sudden manner.

The most common form

Spaghetti can suddenly talk.

is slightly ambiguous between the two, but probably is usually intended to take the former meaning.

The four phrases are correct, though the most common is also most ambiguous.

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 before.

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.