The link that @jacobscros shared is a link to an awesome video of an American female preacher. The whole church fell under the power without her even touching anybody.

Good point @FXKing2012, the account of Balaam's donkey falling down to when it saw the angel was written like the others, which appeared that they bowed down to worship, but surely the donkey didn't fall down to worship, or could it have?

I have never "fallen under the power" myself, but I have had the oppurtunity/priviledge to be the one to conduct some church services. On a few of such occassions, some relatively new people who I myself had invited to church (who had previously not been church goers) "fell under the power" and I didn't even touch them. It happend like this: I was closing my eyes during praise and worship and I heard a loud bang, of someone falling.
I interviwed them afterwards to understand what had happened to them and what made them fall, to understand it all myself. It was clearly the power of God.
There responses were enlightening, but I would rather not share them here.

My advice, go to a church where God's power is real and present. These things are better experienced, than explained.

There were many instances in the bible, when people fell either in the presence of an angel which came from God’s presence, or when Jesus appeared to people after he had descended to heaven and had been glorified.

Example of Saul of Tarsus (Paul) falling "under the power":
Acts 22:7 "And I fell unto the ground, and heard a voice saying unto me, Saul, Saul, why persecutest thou me? "

John the beloved:
Rev 1:17 And when I saw him, I fell at his feet as dead. And he laid his right hand upon me, saying unto me, Fear not; I am the first and the last:

Revelations 22:8 And I John saw these things, and heard them. And when I had heard and seen, I fell down to worship before the feet of the angel which shewed me these things.

Samson’s parents, when they saw an angel:
Judges 13:20 For it came to pass, when the flame went up toward heaven from off the altar, that the angel of the LORD ascended in the flame of the altar. And Manoah and his wife looked on it, and fell on their faces to the ground.

Prophet Ezekiel:
Ezekiel 1:28 As the appearance of the bow that is in the cloud in the day of rain, so was the appearance of the brightness round about. This was the appearance of the likeness of the glory of the LORD. And when I saw it, I fell upon my face, and I heard a voice of one that spake.
Ezekiel 3:23 Then I arose, and went forth into the plain: and, behold, the glory of the LORD stood there, as the glory which I saw by the river of Chebar: and I fell on my face.
Ezekiel 44:4 Then brought he me the way of the north gate before the house: and I looked, and, behold, the glory of the LORD filled the house of the LORD: and I fell upon my face

Even a donkey fell, when he saw an angel:
Numbers 22:27 And when the ass saw the angel of the LORD, she fell down under Balaam: and Balaam's anger was kindled, and he smote the ass with a staff.

The prophet Balaam also fell, when he saw the angel his donkey had seen:
Numbers 22:31 Then the LORD opened the eyes of Balaam, and he saw the angel of the LORD standing in the way, and his sword drawn in his hand: and he bowed down his head, and fell flat on his face.