Firstly is the Jem Fan Club/MTV Jacket offer, which you'll find with every one of the Jem dolls, many fashions, playsets, etc., etc.
 The jacket information can be found here.  The Jem fan club cost $6 to join and you'd get

-Jem and the Holograms Poster, (specific to this fan pack, it is very difficult to find.  Thanks to Shevona for providing it!)
-Rockin' Roadster Key chain (more like a Backstage Pass keychain- (front) (back) thanks Corduroy for the pics!),
-Jem Bandana (Thanks to Rachel for this photo)
-Jem World Tour Iron on Patch (pic 2) (thanks to Heather for the photos!)
-Jem Concert Photo Album.
-Rock Rap magazine (This may be the same thing as the Jem Concert Photo Album, listed above. Thanks to Mandy B. for this scan.)

Canadian Dolls came with a larger MTV offer (French on one side, English on the other), basically the same as the US one, except you could also buy a Jem Wristlocker, basically a wristband that zips open with the Jem logo on it.  I have yet to see an actual wrist locker.  I do not know if they were ever actually available or not.

Promo Tape and Poster offer.
In the United States and Canada, if you bought a Jem doll at participating stores (like Toys R Us) you would receive a Jem tape (with Who Is He Kissing, Jealousy, Universal Appeal and the short and long Jem theme) and a folded up Jem and the Holograms First Year Illustrated Poster as well as a card with the Jem logo and "Free Cassette" written on the front.  This was one of the first promotions.  If the store was out of stock, you could mail in for it.  Check out the commercial! 
 

The Jem and Friends Dream Tour Cassette Offer featured some Jem songs (How you Play the Game, Rock n' Roll is Forever, and Glitter N' Gold) amongst a mixed tape of '80's artists (like New Edition, The Jets, Toto, etc.), and DJ'd by Rio.  This was offered with the second year dolls only.  Some boxes came with a "Smash Hit tape offer" sticker which meant inside you'd get a colour order form to buy the Dream Tour Cassette. Other boxes came with the "Souvenir Program and Tape offer" sticker, which meant inside you'd get the (duh) Jem and Friends Souvenir Program, which is a full colour 14 page magazine featuring bios of all the bands on the Dream Tour cassette.  There are also some lyrics to the Jem songs. The tape cost $1 for shipping and handling.
*Thanks to Kyle for the scan of this tape!

The Glitter N' Gold promo tape
Came with "Glitter N' Gold" (not the theme, but the one from the show), "Back in Shape" and Jem Theme.  This was an instore mail in rebate promotion.  If you bought any Jem doll in 1987, (except Glitter 'N Gold Jem or Rio) you could mail in a coupon (+ UPC code & receipt) to get the tape and a $2.50 rebate cheque.  Offer expired on May 2, 1987.
 
 

You could get $3 off of each, with this coupon, (front) and proof of purchase of Glitter 'n Gold Jem, Rio or the Glitter 'n Gold Roadster.  The rebate check, when received, came with an order form for the Dream Tour Cassette, or Rama Llama (this is the first mention of the llama that I know, and that it is female!)  See Totally Jem for more information and photos about this offer.

Thanks so much to Walter who provided these scans for Jem Vs Pranceatron!

This was given to my friend, who had made connections to people at Hasbro when Jem was still being produced.  It is unlikely that this insert/promotion ever made it to fruition. It would have been included in future doll boxes.
The booklet itself is shaped like airline tickets, with various offers on the pages.  It again makes mention of Jem's world tour of 20 cities on five continents, specifically:

Thanks so much to Walter who provided these scans for Jem Vs Pranceatron!