Discuss and learn French: French vocabulary, French grammar, French culture etc.
I'm actually not so sure about using "cordialement" for an informal letter-- it has more connotations with a semi-formal business letter/e-mail than with, say, a letter/e-mail between friends.
As well as "amicalement", you could use "amitiés", "sincères amitiés", for a closer friendship "gros bisous", ""je t'embrasse". Surely others will have more suggestions too.
In a very formal way, you can also say Je vous prie d'agréer Madame,Monsieur, l'expression de mes sentiments distingués/de mes respectueuses salutations.
This kind of sentence is not really out of fashion but are used for specific situations : covering letter, mail to the administration services,...
They've gone out of fashion in the sense that they're practically never used in e-mails, and a good percentage of commercial correspondence takes place via e-mail.
But as Erwan says, my observation would be that they're still generally used in those instances of formal correspondence still sent by hard copy.