Fortunately
Means "by luck" or "luckily." A very common and slightly more conversational alternative to "afortunadamente."
Literally "thanks to God." Used exactly like "thankfully" to express relief, even in non-religious contexts.
Means "thank goodness" or "it's a good thing that..." It expresses relief that a situation wasn't worse.
I arrived late, but fortunately, the meeting hadn't started.
It was raining a lot, but luckily, I had an umbrella.
I almost missed the bus! Thank goodness I ran.
The exam was difficult, but thankfully, I passed it.
Both 'afortunadamente' and 'por suerte' are universally understood and used throughout the Spanish-speaking world.
Using 'gracias a Dios' is very common in everyday conversation across Latin America (including Mexico, Colombia, etc.), often more so than in Spain. It does not necessarily imply strong religious belief.
'Menos mal' is extremely frequent in Spain to express relief, perhaps slightly more so than in some Latin American countries, but it is understood everywhere.
Saying 'fortunadamente' instead of 'afortunadamente'. — In Spanish, the prefix 'a-' is essential. 'Fortunadamente' is not a word. Always remember to include the 'a-' at the beginning: a-for-tu-na-da-men-te.
Translating 'thankfully' literally as 'agradecidamente'. — 'Agradecidamente' means 'gratefully' (to do something in a grateful manner). To express relief ('thankfully'), you should use 'afortunadamente', 'por suerte', or the very common 'gracias a Dios'.
Using 'suerte' alone when you mean 'fortunately'. — 'Suerte' just means 'luck'. To say 'luckily' or 'fortunately', you need the full phrase 'por suerte'. For example, instead of 'Suerte, tengo mi paraguas', you must say 'Por suerte, tengo mi paraguas'.