Second Year Boxes

In the second year, there were two types; the "diagonal edged" ones and the plain rectangular ones.

Diagonal Edged Boxes

This is a diagonal edged box. 
Each box is particular to the doll that came in it. Second Year boxes have flat fronts, and smaller illustrations. 

Box Backs
There were quite a few different box backs on these, chiefly using shots from the Second Year Jem Catalogue Poster
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All of the Holograms had the same box back. (Aja, Kimber, Shana, Raya, Danse, and Video do), which is the same picture from the Second Year Jem Catalogue Poster.  Notice the instruments are opaque, Aja, Shana and Kimber are wearing hooped earrings, and Raya's stand is not shown holding up the drums.
Synergy; This is the same picture used in the Second Year Jem Catalogue Poster.  Unlike the other deluxe Jem/Hologram dolls of this year, Synergy is only worth 2 Jemstar points. 
Oddly, Flash 'n Sizzle Jem looks like she's wearing satiny loafers but they are just drawn on (thanks Pete B for that info!) It is the same photo (except with the shoes drawn on) as the one used on the Second Year Jem Catalogue Poster.  She is one of the few dolls with photographs on the side panel.  She is also one of two dolls that got the full back of the package for her own photo (Synergy being the other one)
2nd ed. Roxy, Clash, Jetta, Stormer and Pizzazz have the same box back photo, which features the original three Misfits and Clash, but no Jetta!  Again, this box-back picture is different from the one used in the Second Year Jem Catalogue Poster.  Keen eyed fans will notice that the Misfits were only worth 2 Jemstar points.
Glitter N' Gold Jem has the largest doll box.  It's slightly wider than the rest (Glitter N' Gold Rio's remains the same size). Hers and Glitter N' Gold Rio's backs have the same pic.

Rectangular Boxes
 
Rock N' Curl Jem and the Starlight Girls, in keeping with their "cheap" image, came in a regular rectangular box with no flap or horizontal edge.  Rock N' Curl Jems' box was slightly larger than those of the Starlight Girls' but they were proportionately the same. 
At least some of the proposed third year dolls would have been sold in this type of box.
Front of the box.  No Illustrations, but they were particular to each doll as their name was printed directly on it.
The sides have hair styling tips. 
The same box art appeared on the back of each Starlight Girl's box, an illustration of Jerrica and the three Starlight girls.
Rock N' Curl Jem has a photograph on the back (I think the same as the 2nd year catalogue poster photo.) 
International Boxes

So far these are all the 2nd-Year doll boxes I've seen from other countries. There may be others, if you know of any, feel free to let me know!

Belgium
Canada
France
Italy
The Netherlands

Belgium
 


Boxes are written primarily in French and Dutch (Flemish), song titles remain in English. 

1. Doll's name: Depending on the doll, reads: "________ des/van de Holograms" or "________ des/van de Misfits".  See more.
2. Cassette Tape Information: Song titles remain in English, the rest of the writing is in French and Flemish.
3. Hasbro Logo: the same as the US.
4. Truly Outrageous Tag: font is smaller, and reads below that "Vraiment Extravagante." (like the Canadian boxes)
5. Stock Number: Different system from the US
7. Licensing information/Country of manufacture (translated loosely): "1986 Hasbro Inc./Pawtucket RI 02862/Imported for Belgium/Hasbro MB S.A. Digue Du Canal, 109-111, 1070 Brussels."
8. Jemstar Points/Proof of Purchase; Are there, with no indication as to why.

Other Name Changes:
Flash 'N Sizzle Jem/Jerrica was known as Rock 'n Flash Jem/Jerrica
Glitter 'N Gold Jem/Jerrica was known as Rock 'n Gold Jem/Jerrica
Glitter 'N Gold Rio was known as Rock 'n Gold Rio
Rock 'n Curl Jem was known as Rock 'n Roll Jem.

Thanks to Gina for the photos of Clash.

For more on Jem in Belgium, go here.

Canada
 
Photo Needed
Boxes are written in English and French text. 

1. Doll's name: Depending on the doll, reads: "________ des Holograms" or "________ des Misfits". 
2. Cassette Tape Information: Song titles remain in English, the rest of the writing is in French and English.
3. Hasbro Logo: the same as the US.
4. Truly Outrageous Tag: font is smaller, and reads below that "Vraiment Extravagante." (For this reason they resemble Belgian boxes)
5. Stock Number: Same the US
7. Licensing information/Country of manufacture: Hasbro Canada, Inc./Longueuil Quebec/J4G 1G2"
8. Jemstar Points/Proof of Purchase; Are there, and are in French and English

For more on Jem in Canada, go here.

France
 

Boxes are written primarily in French, with English song titles. 

1. Doll's name: Depending on the doll, reads: "________ des Holograms" or "________ des Misfits".   Rock N' Curl Jem becomes Jem Rock 'n Roll, Flash N' Sizzle Jem/Jerrica becomes Jem Rock 'n Flash, Video is Vidéo, The Starlight Girls are simply, Les Starlights, Glitter N' Gold Jem & Rio are Rio & Jem Rock 'n Gold respectively.
2. Cassette Tape Information: Song titles remain in English, the rest of the writing is in French.
3. Hasbro Logo: Not sure, but likely the same as the US.
4. Truly Outrageous Tag: missing completely, replaced with a smaller font that reads "Elle est fantastique."
5. Stock Number: Different system from the US.
7. Licensing information/Country of manufacture: Hasbro S.A., BP 203, 93 153 Le Blanc Mesnil cedex. © 1986 Made in China, tape made in Hong Kong.
8. Jemstar Points/Proof of Purchase; I'm not sure if they were included on French boxes or not.

Check out the catalogue section for more French-only box details.

Thanks to Isabelle for the photo and information in this section.

Italy
 
Photo Needed
Boxes are written primarily in Italian, song titles and dolls' names remain in English. 

1. Doll's name: So far, I've only seen Synergy & Rock 'n Curl Jem in Italian boxes.  They remained the same as the US names.
2. Cassette Tape Information: Song titles remain in English, the rest of the writing is in Italian.
3. Hasbro Logo: Same as US
4. Truly Outrageous Tag: on Synergy, looked the same as that of the US (no "Rock 'n Shock" text, like the first year Italian dolls)
5. Stock Number: Different system from the US
7. Licensing information/Country of manufacture; information needed; likely the same as the first year Italian dolls
8. Jemstar Points/Proof of Purchase: information needed; likely the same as the first year Italian dolls

For more on Jem in Italy, go here.

The Netherlands
 
Photo Needed
While I have yet to see a Dutch language-only second year box, apparently they do exist.  Stefan has the following information about them: 

"2e year dolls in holland were almost only sold with dutch lanuage only but sometimes we got som e english boxes also.  the names were never changed in holland so glitter n gold was kept glitter n gold. the gng roadster and flash nsizzle jem and waterbed were never for sale in holland! i have thiss comfirmed from mb international because i wrote them a letter back in 88 and the send me a list of stuff the sold in holland