Asymmetric Intelligibility

Portuguese and Spanish in Latin America are another example: Brazilian Portuguese speakers usually find it easier to understand Spanish than Spanish speakers do to understand Portuguese. I've heard various theories about this, including that most Brazilians have spent some amount of time formally studying Spanish (while most other Latin Americans haven't studied any Portuguese at all), or that Portuguese has a more complex phonemic inventory than most forms of Spanish so it's harder for Spanish-speakers to recognize certain distinctions in Portuguese.

Within the Portuguese-speaking world, people from Portugal usually find it much easier to understand Brazilians than the other way around, which I've usually heard attributed to the much larger Brazilian TV and film industry, meaning that people in Portugal have probably had quite a bit of prior exposure to Brazilian Portuguese through media.

I also think there's pretty significant asymmetric intelligibility in regional dialects of English.