10th Geup to 1st Geup, I'll just list as [Color][Grade] as that's how it's usually referred to here in Singapore, under the Singapore Taekwondo Federation [all clubs/schools affiliated to the STF are all WTF/Kukkiwon, and I'm under one of the clubs Acme Taekwondo]. These are the forms we need to do at each grade.
White 10 - Kibon Dongjak -.- basically it's just some form created by the STF I think. They call it 'basic movements'.
White 9 - Kibon Taegeuk -.- another form created by the STF I believe, at least that's what it's said at a particular web last time but can't find it now. They call it 'basic taegeuk'
Yellow 8 - Taegeuk Il Jang
Yellow 7 - Taegeuk Ee Jang
Green 6 - Taegeuk Sam Jang
Green 5 - Taegeuk Sa Jang
Blue 4 - Taegeuk O Jang
Blue 3 - Taegeuk Yuk Jang
*Red/Brown 2 - Taegeuk Chil Jang + 1 Taegeuk form randomly picked from Il Jang to Yuk Jang by examiner[s]
*Red/Brown 1 - Taegeuk Pal Jang + 1 Taegeuk form randomly picked from Il Jang to Chil Jang by examiners[s]
Additional info: For the 'odd number geup grades', a stripe of the colour of the next grade, by means of duct tape, is sticked around the edges of the belts.
*In Singapore it's fine to be called a red belt or a brown belt, although brown is the more common term, because the belt we use for 2nd and 1st Geup is maroon in colour. Even the public announcement for local tournaments don't have a unified term for it, some put red some put brown.
1st Dan - Koryo + 2 Taegeuk forms from Il Jang to Pal Jang randomly picked by examiner[s]
2nd Dan - Keumgang + Koryo + 2 Taegeuk forms from Il Jang to Pal Jang randomly picked by examiner[s]
3rd Dan - Taebaek + Keumgang + Koryo + 2 Taegeuk forms from Il Jang to Pal Jang randomly picked by examiner[s]
4th Dan - Pyongwon + Taebaek + Keumgang + Koryo + 2 Taegeuk forms from Il Jang to Pal Jang randomly picked by examiner[s]
5th Dan - Sipjin + Pyongwon + Taebaek + Keumgang + Koryo + 2 Taegeuk forms from Il Jang to Pal Jang randomly picked by examiner[s]
6th Dan to 9th Dan - unable to be tested in Singapore, probably at the Kukkiwon, not sure.**
STF certificates are not automatically Kukkiwon-registered, one has to do the paperwork for Kukkiwon conversion/registration, but it appears that Kukkiwon certification is not needed for regional competitions like SEA Games and Asian Cities Gold Cup.**
Basically only the Taegeuks need to be memorized for gradings, unless the individual intends to coach, which is a different story, disjoint from grading. Whether an individual decides to coach, or is a recognized coach, 10th and 9th Geup forms are not required for gradings after the white belt phase. Personally I can't remember the last part of W9's form because it's been 8 years since I did that.
The STF is mostly, or completely, sport-oriented, and therefore the syllabus is designed towards the competitive side [no extra forms, because the Kukkiwon is using the Taegeuk set now, I guess].