Correct abbreviation of "engineer"

There's no common standard abbreviation for engineer, so generally it would be best to pick one and be consistent.

Eng. is sometimes an abbreviation for engineering in degrees such as B.Eng., Bachelor of Engineering. Therefore, it might be better to use Engr. if it's important to fully disambiguate between the two.

There is no internationally accepted standard. Different countries use different abbreviations. This link lists some of the local forms used in different countries. Some of the common ones are:

Engineer:

Eng. (most common)

Engr.

Er.

Engineering:

Engg. (most common)

Eng.

I don't think I've ever seen any abbreviation of "engineer" by itself as an honorific abbreviation after a person's name, but I've seen plenty of other honorific abbreviations after people's names that include an "E" for engineer:

PE "professional engineer": a person with a state-issued PE license. In the United States and Canada, it's generally illegal to build certain things for use by the public, unless the plans have been signed by a PE (roads, bridges, dams, tall buildings, electric substations, etc.). Typically a person gets a PE license from the state after both 4 years of academic training and also 4 more years of practical experience working under some other PE. I hear that CEng and Eur Ing are the equivalents in other countries. This is analogous to LPN "licensed practical nurse".

CE, ME, EE, IE, ChE, EIT, etc.: A person who has graduated with a university degree in the indicated field of engineering, but may or may not have any practical experience. This is analogous to MSN "Master of Science in Nursing".

MCSE (which has since been renamed MCITP to avoid the controversy mentioned below), SE, NE (network engineer), DE (design engineer), TE, etc.: A person who has some experience applying scientific or mathematical knowledge to technical problems ("engineering"), and has either passed some test related to it, or does these things as part of his day-to-day job (and perhaps that abbreviation is an abbreviation of his job title), but does not necessarily have any academic training. This is analogous to people who have had one-day training in doing CPR and AED, and have plenty of experience "nursing someone back to health with chicken soup", but may not have any other academic training.

IEEE, ASME, IETF, SAE, etc.: a person who is a member of the specified engineering organization. Often many members are college students who hope someday to get a degree in engineering, but have no academic qualifications or practical experience. Sometimes these organizations publish standards that are more influential than any single PE.

There's a pretty big controversy over the word "engineer" -- should people who are not PEs should be allowed to call themselves "engineers"? I think this is analogous to the confusion some people have over "doctors" who have no medical training, but have a doctorate degree in some non-medical field.