The Long Form 吴式太极拳

More correctly referred to simply as the Tai Chi Chuan Form, it is often called the long form to differentiate it from the other weaponless forms.
Here are the names of the movements according to the ‘European branch’ of Wu style tai chi. i.e. 100 movements. As far as I am aware this is the same as the traditional 89 movement form as referred to in “Wu Style Taichichuan” by Wu Ying-hua and Ma Yueh-liang, it is just that some of the movements have been given more or less names.

Thanks to the Paul Brennan translation of “The taiji boxing of Mr. Wu Jianquan – For self-study” for the basic description of the moves.  Modern alterations or differences are given in the comments (please feel free to add your own).

Section I

1. yù bèi shì             预备式          preparation form 
2. tài jí qǐ shì          起势            tai chi beginning form 
3. lǎn què wěi            揽雀尾          grasping the bird's tail 
4. dān biān               单鞭            single whip  
5. tí shǒu shàng shì      提手上势        raise hand and step up  
6. bái hè liàng chì       白鹤亮翅        white crane spreads its wings 
7. lǒu xī ǎo bù           搂膝拗步        brush knee twist step 
8. shǒu huī pí pá         手挥琵琶        hands strum the lute 
9. jìn bù bān lán chuí    进步搬拦捶      step up diverting and blocking fist 
10. rú fēng sì bì         如封似闭        as if closing up 
11. bào hǔ tuī shān       抱虎推山        carry tiger to the mountain 
12. shí zì shǒu           十字手          cross hands 
13. xié lǒu xī ǎo bù      斜搂膝拗步      oblique brush knee twist step 
14. fān shēn xié lǒu xī ǎo bù 翻身斜搂膝拗步 turn body, oblique brush knee twist step 
15. lǎn què wěi           揽雀尾          grasping the bird's tail 
16. xié dān biān          斜单鞭          oblique single whip

Section II

17. zhǒu dǐ kàn chuí     肘底看捶         fist under elbow
18. dào niǎn hóu         倒撵猴           step back repulse monkey
19. xié fēi shì          斜飞势           flying oblique posture
20. tí shǒu shàng shì    提手上势         raise hand and step up
21. bái hè liàng chì     白鹤亮翅         white crane spreads its wings
22. lǒu xī ǎo bù         搂膝拗步         brush knee twist step
23. hǎi dì zhēn          海底针           needle at the bottom of the sea
24. shàn tong bèi        扇通背           fan through back
25. piě shēn chuí        撇身捶           parry and punch
26. xiè bù bān lán chuí  卸步搬拦捶       step up diverting and blocking fist
27. shàng bù lǎn què wěi  上步揽雀尾      grasping the bird's tail
28. dān biān             单鞭             single whip
29. yún shǒu             云手             cloud hands
30. dān biān             单鞭             single whip 

Section III

31. zuǒ gāo tàn mǎ           左高探马     scout on horseback (left)
32. yòu fēn jiǎo             右分脚       kick with right foot
33. yòu gāo tàn mǎ           右高探马     scout on horseback (right)
34. zuǒ fēn jiǎo             左分脚       kick with left foot
35. zhuǎn shēn dèng jiǎo     转身蹬脚     turn body pedalling foot
36. lǒu xī ǎo bù             搂膝拗步     brush knee twist step
37. jìn bù zāi chuí          进步栽捶     step up, planting punch
38. fān shēn piě shēn chuí   翻身撇身捶   turn body, parry and punch
39. shàng bù zuǒ gāo tàn mǎ  上步左高探马 step up scout on horseback (left)
40. yòu fēn jiǎo             右分脚       kick with right foot
41. tuì bù dǎ hǔ             退步打虎     step back beat tiger
42. pī shēn jiǎo             披身脚       opening kick
43. shuāng fēng guàn ěr      双峰贯耳     strike ears with both fists
44. yī qǐ jiǎo               一起脚       two kicks, fist kick
45. fān shēn èr qǐ jiǎo      翻身二起脚    turn and second kick                                                         (or turn body kick with heel)
46. yòu gāo tàn mǎ           右高探马      scout on horseback (right)
47. shàng bù bān lán chuí    上步搬拦捶    step up diverting and blocking fist
48. rú fēng sì bì             如封似闭       As if closing up
49. bào hǔ tuī shān           豹虎推山       Leopard and tiger push the mountain
50. shí zì shǒu               十字手        Cross hands
51. xié lǒu xī ǎo bù          斜搂膝拗步     oblique brush knee twist step
52. fān shēn xié lǒu xī ǎo bù 翻身斜搂膝拗步  turn body, oblique brush knee twist step
53. lǎn què wěi               揽雀尾         grasping the bird's tail
54. xié dān biān              斜单鞭         oblique single whip

Section IV

55. yě mǎ fēn zōng                野马分鬃      parting wild horse's mane
56. shí zì yě mǎ fēn zōng         十字野马分鬃   cross hands, parting wild horse's mane
57。shàng bù zuǒ yù nǚ chuān suō   上步左玉女穿梭 step forward, jade girl works the shuttle, left
58。zhuǎn shēn yòu yù nǚ chuān suō 转身右玉女穿梭 turn body, jade girl works at shuttle, right
59。shí zì yě mǎ fēn zōng          十字野马分鬃   cross hands, parting wild horse's mane 
60。shàng bù zuǒ yù nǚ chuān suō   上步左玉女穿梭 step up, jade girl works the shuttle, left
61。zhuǎn shēn yòu yù nǚ chuān suō 转身右玉女穿梭 turn body, jade girl works at shuttle, right
62。shàng bù lǎn què wěi           上步揽雀尾    step forward, grasping the bird's tail
63。dān biān                       单鞭          single whip
64。yún shǒu                       云手          cloud hands
65。dān biān                       单鞭          single whip

Section V

66。xià shì              下势     downward posture 
                        (蛇下势 - shé xià shì - snake creep down)
67。jīn jī dú lì         金鸡独立  golden cockerel stands on one leg
68。dào niǎn hóu         倒撵猴    step back repulse monkey
69。xié fēi shì          斜飞势    flying oblique posture
70。tí shǒu shàng shì    提手上势  raise hand and step up
71。bái hè liàng ch      白鹤亮翅  white crane spreads its wings
72。lǒu xī ǎo bù         搂膝拗步  brush knee twist step
73。hǎi dǐ zhēn          海底针    needle at the bottom of the sea
74。shàn tōng bèi        扇通背    fan through back
75。piě shēn chuí        撇身捶    parry and punch
                         撇【piē】 cast aside; throw overboard; neglect; skim. 
                         撇【piě】 throw; fling; cast; left-falling stroke (in Chinese characters).
76。xiè bù bān lán chuí  卸步搬拦捶 step up diverting and blocking fist
77。shàng bù lǎn què wěi 上步揽雀尾 grasping the bird's tail
78。dān biān             单鞭      single whip
79。yún shǒu             云手      cloud hands
80。dān biān             单鞭      single whip

Section VI

81。zuǒ gāo tàn mǎ              左高探马       scout on horseback (left)
82。yíng miàn zhǎng             迎面掌         palm goes to meet face
83。shí zì bǎi lián             十字摆莲       one handed lotus
84。lǒu xī ǎo bù                搂膝拗步       brush knee twist step
85。jìn bù zhǐ dāng chuí        进步指裆捶     step up, punch to crotch
86。shàng bù lǎn què wěi        上步揽雀尾     step up grasping the bird's tail
87。dān biān                    单鞭          single whip
88。xià shì                     下势          downward posture
89。shàng bù qī xīng            上步七星       seven stars
90。tuì bù kuà hǔ               退步跨虎       step back ride tiger
91。zhuǎn shēn pū miàn zhǎng    转身扑面掌     turn body, hit face palm
92。fān shēn shuāng bǎi lián    翻身双摆莲     turn, double handed lotus
93。wān gōng shè hǔ             弯弓射虎       curve bow shoot tiger
94。zuǒ gāo tàn mǎ              左高探马       scout on horseback (left)
95。yíng miàn zhǎng             迎面掌         palm goes to meet face
96。fān shēn piě shēn chuí      翻身撇身捶     turn body, parry and punch
97。shàng bù zuǒ gāo tàn mǎ     上步左高探马    step up scout on horseback (left)
98。shàng bù lǎn què wěi        上步揽雀尾     step up grasping the bird's tail
99。dān biān                    单鞭          single whip
100。hé tài jí                  合太极        closing tai chi