Correct syllabification in (American) English

The dirty little secret of English is that syllable boundaries mostly do not matter (unlike other languages). What is important is the syllable nuclei which are easily identified either as the vowel or a syllabic consonant (such as / n / in 'sudden'.)

As @robert says, the Onset Maximization Principle is most commonly adopted when trying to determine which consonants belong to the nucleus. This principles states, that all things being equal, consonants should belong to the start of the syllable.

However, this principle is subject to a number of phonotactic constraints. Such as a prohibition of a short stressed open syllable. These constraints are generally derived from what is observed in monosyllabic words (because we know those are possible) as well as from an attempt to have a system that is consistent.

This latter aim lead the phonetician John Wells to offer an alternative syllabification principle, stated thus:

(1) Subject to certain conditions, consonants are syllabified with the more strongly stressed of two flanking syllables.

(2) Where adjacent syllables are of equal grade, consonants are (again subject to stated conditions) syllabified with the leftward syllable.

This might lead to violations of certain phonotactic principles such as syllabifying 'limber' as limb/er. But mb is not possible in English as a syllable-final cluster, so the syllabification is lim/ber. And so on.

As a result, the two main pronunciation dictionaries of English (Cambridge and Longman) both use a very different syllabification pattern.

Personally, I feel that the Onset Maximization Principle is more often in consonance with native speaker intuitions (although I don't have the literature to back it up) and would also be more beneficial to non-native speakers because it results in syllables with simpler clusters. E.g. 'hospital' is more helpful as 'hos-pi-tal' than 'hosp-i-tal'.