Nor or Nor-nor: Norway. Sometimes also referred to as "Norge", which is just the Norwegian word for his name.
A mochi with an Emoticon resembling America from the author's blog (that became very popular in Japanese fanarts) is nicknamed "Amerimochi" or "Mochimerica"
Wan-nyan (amongst Chinese-speaking audiences), Wan-chan, "Mei Mei" — Taiwan. The first two are based on the second half of the word "Taiwan"; the last one means "Plum Blossom" in Chinese, which she wears on her head, and is also the flower symbol of Taiwan.
Mei Mei in Mandarin also means "little sister" which is fitting if China's the older "sibling"
The Forehead Four — Denmark, Thailand, Netherlands, and Australia, known as such for their Wild Hair and prominent foreheads. Spiky Hair Squad is also not uncommon in order to different them from Germany, Austria and Korea.
Gilbo — Prussia, after his human name, Gilbert Beilschmidt.
If anyone becomes friendly with him, expect the name Gil to show up. This is annoyingly prominent in PruCan.
Gilbird — The yellow chick seen sitting on Prussia's head during the 2009 April Fool's event.
The Bad Touch Trio (or BTT) — The increasingly popular OT3 of Prussia, Spain and France. Also known as the "Bad Friends Trio" and the "Bad Company Trio".
Other trios include The Outcasts (America, England, Japan; named such for isolationism) and The Pitiful Brothers Trio (Prussia, England, Denmark for being bad influences).
Recently, the nickname Awesome Trio (America, Denmark, and Prussia) has gotten popular.
Also, FACE for the family unit/foursome of France, America, Canada, and England.
Also there's FrUKUS: France/England/America. Often the only answer to the FrUK (France/England) Vs USUK (America/England) debate.
The Magic Trio, consisting of England, Norway and Romania, has been popping up, due to their ties with magic and/ or supernatural things (it hasn't been confirmed yet as to whether Norway actually does magic).
JOKER — US x UK, from Jones & Kirkland. (It's more obvious in Japanese where it's pronounced the same as "Joker.")
Iggy — UK. From "Igirisu," which is is "Britain" in Japanese. The Western fandom took this a step further and uses "Iggy" as America's nickname for England in fanfics, though technically it was France who coined the term in the 2007 Christmas Bloodbath strips.
MKC — The nickname for the Hetalia's theme song, "Marukaite Chikyuu"
Katyusha (or Katya for short) as Ukraine's human first name; Katyusha is a Russian name (diminutive of "Yekaterina" aka "Katherine") and a term for rocket artillery.
Pubertalia — Italy during, well... puberty, from the strip when his voice changes from his normal Chibitalia voice and he is revealed to be male. Other nicknames that end with '-talia' also exist.
Nyoitsu- female Germany, a combination of 'Nyotalia' (a fanon term for Hetalia genderbending, "nyo" being one of the readings of the kanji for "woman") and the Japanese word for Germany (Doitsu). There's also 'Koruko' for female Russia.
Also, Mangary for Male Hungary.
That F*cking Island- A derogatory term used for the island that appears in the beach-themed Stock Footage in various episodes of the anime. To be fair, the island did have basis in the manga, but as a minor setting that appeared in about three short strips (without the beach battles).
Chibimano- The younger version of South Italy (Romano), referred to by this to differentiate him from his brother, although both would technically be "Chibitalias".
Also from the Bloodbath, Mr. Assbitch, the random extra seen staring at naked Parallel!Spain's ass.
The Japanese fandom, which has much stricter guidelines for the fans to follow than the English fandom, is really big on this, to the extent that the fan community on some websites (Nico Nico Douga and Pixiv come to mind) forbid the use of nation names. This is mainly so that non-fans who might find Hetalia offensive can't stumble on fanarts/fanvids/whathaveyou accidentally.