Nouns:
* Jack-o'-lantern
* Jailbird
* Jambalaya
* Jamboree
* Jeans
* Jet-setter
* Jigsaw
* Junk food
* Jumper (clothing)
* Jury
Adjectives:
* Jet-black
* Jaw-dropping
* Jobless
Verbs:
* Jettison
* Joggle
* Jump-start
Other:
* Just-in-time (adverbial phrase)
* Join-the-dots (game)
This is just a small selection, and there are many other compound words starting with "j" depending on your specific criteria (nouns, verbs, etc.) and the level of formality desired.