The Gulf states come up most often — the United Arab Emirates, Qatar, and Kuwait all still require attestation through their consulates, as do Jordan, Egypt, Lebanon, and Iraq.
Elsewhere, Taiwan, Vietnam, and Thailand currently take the legalization route. Vietnam and Thailand both have accession dates scheduled, so check the country lookup before planning around them.
We hold dedicated pages for the destinations we handle most: UAE, Qatar, Kuwait, Jordan, Thailand, and Vietnam.