With comma splices replacing line breaks, e.g.:

Greg Yourp
137 Stiener St. Apt #3
Boston MA 02134-5623
USA

becomes:

Greg Yourp, 137 Stiener St. Apt #3, Boston, Mass., 02134-5623, U.S.A.

Note that there are no commas in the city state zip line in the envelope format, in accordance with postal guidelines, but there are when an address is written as inline text. Older custom is to include them on envelopes and to use a longer abbreviation for the state. Guidelines were updated to make addresses more easily readable both for machine readers and human sorting machine operators.

(Name and address are made up, but I think I got part of the ZIP code right)

Boston, Mass., 02134-5623, U.S.A.

More properly, should be

Boston, MA 02134-5623, USA

The "oldstyle" state abbreviations—Mass., Penna., Tex., etc.—may be considered proper AP style, but they introduce unnecessary confusion into the postal address process. And, FWIW, to avoid confusion, using the middot or periodcentered characters with added space on either side is probably preferable, given that a comma is used in the city-state-zip segment.

Here's how I do it:
5214 Livermore St, Palmdale, MA 11208 USA

hhp

I've long ago abandoned the long state abbreviations too, but I still see them in print often enough.

You're "allowed" to use the two-letter postal code, just not in running text.

hhp

Ah! Thanks for the swift answers guys!