I personally wouldn't. Regex has its place, but if it takes over 20 characters to describe its purpose, then there must be a better solution.
Looks like you are using Java, so the Apache Commons Validator library should help out. It can validate emails and your could make it so that it doesn't use IP addresses or localhost as valid emails.
If you still feel this is best, then I would wrap it at matching parentheses, because those specify groups. Also at square brackets if necessary. If there is a plus or star at the end of either of them, I would put the new line after that, because those specify whether you want it to repeat. Same thing for curly brackets.
Pattern cachedEmailRFCChecker = Pattern.compile(
"^\\A(?=[a-z0-9@.!#$%&'*+\\/=?^_`\\{|\\}~-]{6,254}\\z)"
+ "(?=[a-z0-9.!#$%&'*+\\/=?^_`\\{|\\}~-]{1,64}@)"
+ "[a-z0-9!#$%&'*+\\/=?^_`\\{|\\}~-]+"
+ "(?:\\.[a-z0-9!#$%&'*+\\/=?^_`\\{|\\}~-]+)*
+ "@(?:(?=[a-z0-9-]{1,63}\\.)"
+ "[a-z0-9](?:[a-z0-9-]*[a-z0-9])?\\.)+"
+ "(?=[a-z0-9-]{1,63}\\z)[a-z0-9]"
+ "(?:[a-z0-9-]*[a-z0-9])?\\z$"
);