陈氏混元38式太极刀
Initially copied with minor edits from other sites but I have yet to complete the Chinese tonal marking and appropriate literal translations with footnote. Also the sectioning is my own attempt, as far as I know, there isn't any official organization of the form into sections. 

Section 1
1. 起式 Qi~ Shi\
   Starting Move
2. 护心刀 Hu\ Xin- Dao-
   Protecting Heart with Saber                    
3. 青龙出水 Qing- Long/ Chu- Shui~
   Blue Dragon Comes Out of Water                
4. 风卷残云 Feng- Juan~ Can/ Yun/
   Wind Blows Scatters Clouds               
5. 白云盖顶 Bai/ Yun/ Gai\ Ding~
   White Clouds Cover the Head               

Section 2
6. 黑虎搜山 Hei Hu Sou Shan
   Black Tiger Searches Mountain               
7. 苏秦背剑 Su Qin Bei Jian
   Su-Qin Carries the Sword               
8. 金鸡独立 Jin Ji Du Li
   Golden Rooster Stands On One Leg               
9. 迎风斩草 Ying Feng Zhan Cao
   Cut Grass Against the Wind                
10.腰斩白蛇 Yao Zhan Bai She
   Cut White Snake at the Waist

Section 3
11. 日套三环 Ri Tao San Huan
    Capture Sun with Three Rings                    
12. 拨云望月 Bo Yun Wang Yue
    Push Away Clouds to Look at Moon                
13. 拨草寻蛇 Bo Cao Xun She
    Part Grass to Seek the Snake                    
14. 青龙出水 Qing Long Chu Shui
    Blue Dragon Comes Out of Water                
15. 风卷残云 Feng Juan Can Yun
    Wind Blows Scatters Clouds
    
(followed by unnumbered move: 腰斩白蛇 
 Cut White Snake at the Waist)

Section 4
16. 力劈华山 Li Pi Hua Shan
    Forcefully Split Hua-Mountain 
17. 雁别金翅 Yan Bie Jin Chi
    Goose Tucks Its Golden Wings
18. 夜叉探海 Yie Cha Tan Hai 
    Night Demon Probes the Sea
19. 翻身砍 Fan Shen Kan
    Turn Around and Chop 
20. 回身再砍 Hui Shen Zai Kan
    Turn Back to Chop Again 

Section 5
21. 黄龙三搅水 Huang Long San Jiao Shui
    Yellow Dragon Stirs Water Three Times
22. 退步分水式 Tui Bu Fen Shui Shi
    Step Back to Part the Water 
23. 双震脚 Shuang Zhen Jiao
    Double Stomp Feet
24. 玉女穿梭 Yu Nu Chuan Suo
    Jade Lady Works At Shuttle
25. 腰斩白蛇 Yao Zhan Bai She
    Cut White Snake at the Waist

Section 6
26. 野战八方 Ye Zhan Ba Fang
    Battle Eight Directions at Night
27. 连环刀 Lian Huan Dao
    Circular Slashing Saber 
28. 败势撩阴刀 Bai Shi Liao Yin Dao
    Feint Retreat then Low Crotch Cut  
29. 护心刀 Hu Xin Dao
    Protecting Heart with Saber 
30. 白鹤亮翅穿心掌 Bai He Liang Chi Chuan Xin Zhang
    White Crane Spreads Wings Palm Strike thru Heart 
                             
Section 7
31. 反背刀 Fan Bei Dao
    Turn Back and Chop
32. 独立式 Du Li Shi
    One Legged Stand Posture 
33. 披身斜挂 Pi Shen Xie Gua
    Cover Body Chop and Hang Slanted 
34. 横扫千军 Heng Sao Qian Jun
    Sweep across Thousand Soldiers 

Section 8
35. 刺刀开合 Ci Dao Kai He
    Saber Thrust and Open Close 
   (或 指南针开合式 Zi Nan Zhen Kai He Shi
    or South Pointing Needle Open and Close)
36. 夜叉探海 Ye Cha Tan Hai
    Night Demon Probes the Sea 
37. 白猿献果 Bai Yuan Xian Guo
    White Ape Presents Fruits
38. 怀中抱月收式 Huai Zhong Bao Yue Shou Shi
    Cradle Moon in Bossom Closing Move

Hunyuan Saber section 1, 2 by Brian

Hunyuan Saber section 3, 4 by Raymond

Hunyuan Saber section 7, 8 by Jarret