First, let me make clear this section is for Jem _licensed_ merchandise only, I'm not really interested in lighters, mousepads, address labels and snowglobes (etc etc) that people have made on their computer to sell on eBay.  Any knock-off items lucky enough to be posted on this site will go either in the knock-offs section or their country of origin. That said...
Jem had a plethora of products licensed by Hasbro, focusing mostly on school items, games, party supplies, clothing and the like.  The following is a list of licensed Jem items I know about that were released in the US/Canada.  Not surprisingly, Europe, Australia, South America and possibly other areas had their own unique items, to see information on those, go to International Jem.  I am always interested in hearing about new Jem items, if you have any infromation to offer, feel free to e-mail me! 

School Items/Bags/Lunch Kits, etc
Games & Puzzles
Watches
Party Supplies
Cosmetics & Grooming
Costumes & Children's wear
Other Jem items

Lunchkit (Alladin) 
The thermoses are small, color coded to their lunch kit and have the Jem logo on them.  The kits are vinyl & came in two different colours.

purple
yellow

Snack Pack (SGI) In Package Back of Package
Basically a small backback with the Glitter N' Gold Jem logo, dated 1987.  Comes with a matching (but no Jem logo) zippered lunchbag that fits inside the front pocket.  Thanks to Monica for sending photos of the package!

Back Pack The following information is quoted from the catalogue: "Woven nylon backpack features screen print of Jem's group, the Holograms (we've even riveted a plastic guitar to the front).  Top zip, padded adjustable shoulder straps, locker loop. 12 X 13.5 X 3". "
(thanks to thejaggirl2000 for this photo & info!)

Thermos
Possibly belonging to the Snack Pack above.  A small pink thermos with white cap, & the Glitter and Gold Jem logo on front, dated 1987.  I bought mine in Canada, I've never seen another.

Duffel Bags- see Jem Sleeping Bags.

Spindex stationery supplies (I only have seen the crayons, on the back of the package it tells what else they made.)

Pop-A-Point crayons
Pop-A-Point Pencils
Diecut erasers
Pencil toppers
Pencil Pouches Not sure if there was more than the one pictured, or if they were sold separately.
Ball-point pens
Jumbo Erasers
Figurine Erasers
Spindex School Kit, bubble on card, contains
        1) Jem Pencil case (pink with Jem standing in front of Rockin' Roadster),
        2) Purple Ruler with pink sticker, has pictures of Jem, Aja, Pizzazz and Stormer;
        3)Purple round pencil sharpener, sticker of Jem on front,
        4)Pink eraser with sticker of Pizzazz on front

Games (Milton-Bradley)
All come with game tapes.  5 songs per tape, all on one side.  The other side has little snippets of the songs (2 seconds of the chorus, for example) so you can use the tapes to play the game.  There aren't any instrumentals on these tapes.

Fashion Flash (yellow box); Features re-drawn pics of all the Holograms wearing the first year line of fashions.  Kinda neat.
Rock and Romance (pink box); Who does Rio really love?  Features magnetized cards that repel or attract each other.
Concert Clash (purple box); Collect record tokens (uses real Jem/Misfits song titles) and become the most popular group.  A Jem-Misfits rivalry game.

The Misfits (The Misfits Illustrated poster)
The Holograms (1st year holograms box art)
Rio (1st year Rio box art)
Jem/Jerrica (Basically the 1st year Illustrated Jem Poster)

Image changes from Misfits to Holograms
Image changes from Jem to Jerrica

Watches

Pink and white keyboard design
Orange and Yellow audio tape design
Green Record design

Party Pak (came with plates, cups, lootbags, table cloth, etc)
Table Cloth
Party Invitations
Loot bags
noise blowers
Paper Plates
Napkins
Balloons
hats
Cups
Cake Decoration (candy letters)

3 peice dresser set: hot pink plastic comb, brush and mirror set, child size. (ARC) The EASIEST non-Doll related toy to find!
Glitter N' Gold Travel Kit (contains 60 mL bottles each of Cologne, Shampoo and Bubble Bath, has a cardboard folding handle on top for easy carrying.) Dated 1987 and licensed by Hasbro.  This picture is from a Canadian version which may be differently named than the US ones.*
Glitter N' Gold Cologne (not sure if this was actually sold seperately)
Jem On Tour Cosmetic Set (Cosrich)
Glamour 'n Glitter Cosmetic Set (Cosrich)
Nail tint n' Decals Cosmetic Set (Cosrich)
Frosted Lip Gloss n' Decals Cosmetic Set (Cosrich)
Lip Pot Duo and Decals (comes in a round 45 rpm record shaped package, neat!
Reach for the Stars Cosmetics Set*" dated 1986 Hasbro Inc., below that it says Giftique Div. Cosrich Inc., Perth Amboy, NJ.  The package contains one bottle of 1/2 fl oz cologne (fl is yellow in color); one necklace, large irridescent pink plastic star in center of necklace with many smaller stars on each side, the stars are yellow, pink and purple in color.  One set of matching irridescent pink plastic star shaped earrings. Plastic handle on top of box for carrying.*
Deluxe Take-Along Vanity Set #1 (Cosrich) Came with cosmetic bag, compact mirror, comb and brush (they aren't the same ones that came with the 3 piece dresser set) (Thanks thumper for the photo!)  This one has a pale pink cosmetic bag, with the Jem logo in pink and yellow & "confetti" around it. The brush has the Jem logo on a pink and yellow graded background.
Deluxe Take-Along Vanity Set #2 (Cosrich) (Came with cosmetic bag, compact mirror, comb and brush (they aren't the same ones that came with the 3 piece dresser set) (Thanks thumper for the photo!)  This one has a hot pink cosmetic bag with the Jem logo in a white circle. The brush has the Jem logo on a white background. 
Glitter N' Gold Nail Polish and Lip Shine(contains pink nail polish and lip gloss) Dated 1987 and licensed by Hasbro.  This picture is from a Canadian version which may be differently named than the US ones.

Costumes (Ben Cooper) 

Boxed Halloween Costume with mask and plastic Jem dress!
Halloween Costume on a hanger; same as above. 
I have seen a variant of these, some have "sparkly" earrings, others have plain red ones.

Screen-Printed pink, longer-length skimp top:  Wear with stirrup pants or as a minidress (stirrup pants are generic and could be bought separately).
Screen-Printed white top  long sleeved shirt with Jem logo and keyboard design. (skirt shown is generic and could be bought separately).
Screen-Printed Black skimp top: Black with Jem logo and musical notes (stirrup pants are generic and could be bought separately).
White and Black Tank Dress, with Jem wearing a bikini sitting on a Jeep (!)  Thanks to Monica for this photo!
Jem Child's shorts set: "the t-shirt was white with jem in a shirt and shorts hitting a tennis ball, an in the back ground there was roses and a crowd going wild with the jem logo on there somewhere. and the shorts were pink with green tennis rackets and yellow tennis balls on them, if I remember correctly, they were like stripes up and down on the shorts."
Bright Fuscia long sleeved/long length sweat top/mini dress, with small Jem logo.
Black long sleeved shirt with Jem holding mic, Jem logo in bottom right corner. 
Shirt, Pants & star earrings set from JC Penney's
Sweat pants; Jem singing into a microphone drawing on one leg and a Jem logo on the back.
Sleeveless Shirt, white with pink ringers, has Jem logo and the "Rio/Jerrica on phone/Jem triangle art printed on it. 
Long-sleeved Polo style shirt, white with pink collar, with redrawn box art of Jem and the Holograms as well as the Jem logo. Says "Music is Magic". 

Nightshirt #1: white with lavender trim, of Flash N' Sizzle Jem sitting on a huge guitar
Nightshirt #2: white with the Jem Star Stage art on the front.
Nightshirt #3: White, Jem standing in front of the Star Stage, redrawn art. 
Flipside Pyjamas with Jem on the front and Jerrica on the back, redrawn box art.
Nightgown and Doll sized nightie set #1: White with lavender (ringer style) nightie with Jem Logo/stars and Jem leaning on her head on her hand.  The doll nightie was about Cabbage Patch Kids' sized. Made by GIRLS FASHIONS, USA, Hasbro, 1987. There were other toy lines done this way, Rainbow Brite for example.
Nightgown and Doll sized nightie set #2: White with lavender (ringer style) nightie with Rio box art, and Jem standing in front of it with her arm across Rio. The doll nightie was about Cabbage Patch Kids' sized. Made by GIRLS FASHIONS, USA.

Slippers
Dress Shoes
Glitter N' Gold Jem Galoshes  They somehow made rubber boots glamorous enough for Jem...
Jem socks- silver tinsel with Jem 1st ed. illustrated poster image- COOL!
Winter Boots: white nylon with "confetti" design, small image of Jem on the front. Tread has Jem logo, stars, musical notes! 

Sunglasses ("cats-eye" style, teal or mauve), on bubble card.
Record-shaped Purse : Quote taken from the catalogue: "Jem screen-printed record-shaped bag is a real groove! Vinyl backed rayon bag has 8" diameter, is one & a half inches deep.  Zip closure.  Attached coin purse has three inch diameter."

Sleeping Bag w/matching Duffle Bag (1986) Orange with Jem singing into a microphone.  Thanks to thejaggirl2000 for this scan!
Sleeping Bag w/matching Duffel Bag Glitter and Gold Jem with Rio. Thanks to Mandy B. For this scan from the 1987 Sears Wishbook!
Bed Tent: Thanks to Mandy B. For this scan from the 1987 Sears Wishbook!
Jem PVC, it reads, 1986 Hasbro Inc. Hong Kong.  Were made to be sold in toy stores, but as Jem was not doing well by this point, they were sold off as cake decorations.  There were other PVC characters made that were sold in Argentina (I've seen Pizzazz, Rio and Aja so far).  Thanks to Monica for this photo.
View Master 3 reels on card.  I like this set because it tells the story of the first five episodes but isn't quite so subtle with Ashley's fate..."Go to the Starlight Drive-In or Ashley will die," Eric telephones.  Yeesh!
Viewmaster gift set, comes in nicely re-drawn Jem themed box, with viewmaster and reels.  Thanks Redhotcherrie for this photo!
Jem Presto Magix (boxed)  "Contains a 12"x24" Action Poster, Transfer Sheet with over 30 Transfers, and a -Special Magix Stick. Made by American Publishing Corporation." (thanks to Joyce for letting me use her scan!)
Jem Presto Magix (bagged) have only seen a bad scan of these, looks 8X10 with redrawn Jem and Aja on front.* Scans Courtesy of Joyce Allan
Holograms Magic Slate  (Golden) 
Jem/Jerrica Magic Slate  (Golden)
Jem Towel; Licensed; Notice Jerrica is in the Star, (not Rio) and Shana has a white skintone.  Not redrawn totally well but still cool. Thanks Mandy B and Panda for the picture!
Jem Doll-sized nightie: I believe made for Cabbage Patch Kid-sized dolls.  Thanks to Monica for the scan!