Goku (First Appearance): 10
He already has twice the power of an ordinary person. What’s more, his body is tough enough to repel a gun’s bullet.
Goku (Oozaru): 100
His battle power becoming ten times its usual, he can even pulverize a 30 cm stick steel wall. His has the destructive power of a battleship’s main gun.
Goku (22nd Tenkaichi Budoukai): 180
Experiencing much training and battle, his ability has substantially increased. His loosing the championship was merely a difference in fate between him and Tenshinhan.
Kame-sennin (Jacky Chun): 139
He powered up through training that he kept secret from his pupils. He brilliantly fulfilled his role building a bridge to a new era.
Tsuru-sennin: 120
The man who had previously competed with Kame-sennin as a rival. However, in actual ability it seems Kame-sennin has a slight lead on him.
Tenshinhan: 180
He attacks Goku with superhuman high-level techniques and power. Their contest is practically even.
Goku (Versus Piccolo Daimao): 260
Having drunken the Super God Water and awoken his hidden power, his ability becomes on par with Piccolo Daimao. The death-match develops with Tenshinhan’s assistance.
Piccolo Daimao: 260
With his youth restored, he becomes even more powerful. His power, which easily blows away a city, rivals that of a small nuclear bomb.
Goku (Versus Raditz): 416
At the appearance of an unprecedented strong opponent, he teams up with Piccolo. However, in a serious battle it’s no contest, and in exchange for victory Goku loses his life.
Piccolo: 408
Unfastening the training equipment, he stands to fight at full power. The Makankosappo that he fires from his fingertips is equivalent to 1,330.
Son Gohan: 1~1,307
Although it changes greatly based on his emotions, his hidden power already surpasses his father Goku. He is still four years old.
Kuririn: 206
Through straightforward training and talent that’s first-rate for Earthlings, he has surpassed his master Kame-sennin. Afterwards, he holds up on the frontlines of battle.
Raditz: 1,500
He toys with Goku and Piccolo with incredible power and speed. However, nevertheless he is still just a low-level warrior.
Goku (Versus Vegeta): 8,000
Receiving training from Kaio, his ability has revolutionarily increased. From this time onwards, the Kaio-ken and Genki-dama become Goku’s reliable weapons.
Nappa: 4,000
Saibaiman: 1,200
Vegeta: 18,000
Kuririn: 1,770
Yamcha: 1,480
Chaozu: 610
Tenshinhan: 1,830
Piccolo: 3,500
Son Gohan: 2,800
Goku (Kaio-ken x4): 32,000
Goku (Arrival on Planet Namek): 90,000
Training under gravity a 100 times that of Earth, he breaks down the limit of the Saiyans of the past. With the Kaio-ken as well, he becomes able to endure up to x10.
Son Gohan: 14,000
Kuririn: 13,000
Vegeta: 30,000
Goku (Versus Freeza: 3 million)
As a result of having his wounded body restored in a medical treatment machine, Goku achieves a super power-up that surprises even him. Awakening his pride as a Saiyan, he faces the decisive battle.
Freeza 50%: 60 million
Freeza 100%: 120 million
He transforms into his final form, and overwhelms Goku with half of his ability. However, he unleashes his full power at the appearance of the Super Saiyan.
Goku (Super Saiyan): 150 million
The legendary warrior Super Saiyan finally awakens. As well as having battle power 50 times that of his normal state, he overwhelms even Freeza.
What about the change in Goku’s battle power after that?
Even after the battle with Freeza, formidable enemies that surpassed human knowledge appeared before Goku one after the other. The power-ups from having wounds healed became small*, but transformations and fusions came to increase the battle power of Goku and the others. To the point where they could no longer be gauged with numerical values…
From the Daizenshuu 7 character dictionary, we having the following new ones (that I know of):
Kyui: 18,000
Dodoria: About 22,000
Zarbon (normal form): About 23,000
Piccolo (merged with Nail): Over 1,000,000
The 1989 double issue of Weekly Jump has a special pull-out poster thingy on battle powers (though they’re called “approximate battle ability” rather than battle power). It seems this list was the source for many of the battle powers in Daizenshuu 7, or they share the same source. Unless otherwise noted, all numbers are from the Saiyan arc, as the issue was printed while the fight with Vegeta was still going on (this may explain why Popo’s battle power is so darn high: he got stronger training the Earthlings). Here are all the ones not also found in Daizenshuu 7:
Son Goku (18 years old): 910
Kami: 220
Chi Chi: 130
Yajirobe: 970
Cyborg Tao Pai Pai: 210
Kame-sennin (Muten Roshi): 180
Karin: 190
Mister Popo: 1,030
Kaio: 3,500
There’s also supposed to be an issue of V-Jump with battle powers as well, that contains the following:
Tao Pai Pai (first appearance): 110
Gyuumao: 97
Chaozu (unclear when): 84
Vegeta (after the Recoome fight): 250,000