According to the following sources it is e.g. in BrE and e.g., in AmE

  • abbreviation for exempli gratia: a Latin phrase that means "for example". It can be pronounced as "e.g." or "for example": You should eat more food that contains a lot of fibre, e.g. fruit, vegetables, and bread. (Cambridge Dictionary)

According to the Chicago Manual of Style:

  • According to the Chicago Manual of Style, it's "e.g." and it's not italicized. It's an abbreviation, so just as you would abbreviate United States to U.S., you do the same with e.g.

  • (I mention the point about not italicizing because e.g. is an abbreviation for a Latin phrase, and foreign language words and phrases are sometimes italicized. However, when they are very common—e.g., "nom de plume"—you don't italicized. Such is the case with e.g. and it's cousin, i.e.

According to Wiktionary:

  • it's "e.g." and it's not italicized. It's an abbreviation, so just as you would abbreviate United States to U.S., you do the same with e.g. The list of examples following e.g. should not be exhaustive (in that case, i.e. should be used) and should not be followed by et cetera or etc. as this is a tautology. (Tautologies do have their place, but use etc. in this context with care.)

  • In American English a comma should follow e.g. For example: Female marsupials (e.g., kangaroos, opossums) have a pouch.

  • In British English no comma should follow e.g. For example: Female marsupials (e.g. kangaroos, opossums) have a pouch.

Note also that:

  • A punctuation mark always precedes e.g. I like sweet foods, e.g. chocolate. (cf. I like sweet foods, for example chocolate.) I like sweet foods (e.g. chocolate and marzipan) and eat them often.

From wiktionary :

e.g.

Alternative forms

eg., eg (informal)

Usage notes

  • In American English a comma should follow e.g. For example:

Female marsupials (e.g., kangaroos, opossums) have a pouch.

  • In British English no comma should follow e.g. For example:

Female marsupials (e.g. kangaroos, opossums) have a pouch.

  • A punctuation mark always precedes e.g.

I like sweet foods, e.g. chocolate. (cf. I like sweet foods, for example chocolate.)