It's not that common for Western Bands to make it in Japan, even popular ones. Some of them did though. Here are 20 examples of those bands.
(Bands listed in alphabetical order. Under each band's picture, their most successful album and most successful single in Japanese charts, are listed.)
1) Asia

Alpha (1983) #4
No Data.
2) Bon Jovi

These Days (1995) #1
No Data. (Although Bon Jovi's singles sold very well in Japan)
3) Cheap Trick

Dream Police (1979) #4
I Want You To Want Me (1977) #1
4) Danger Danger

Screw It! (1991) #67
No Data.
5) Hanoi Rocks

I couldn’t find anything particular about charts, but the band is very popular in Japan, to the point they released albums/singles exclusively for Japan.
6) Helloween

Master Of The Rings (1994) #6
I Don't Wanna Cry Anymore (1993) #1 (Apart from it, they had seven other #1 hits in Japan)
7) Iron Maiden

The Final Frontier (2010) #5
No Data.
8. Journey

Frontiers (1983) #3
Who's Crying Now (1981) #4
9) Men At Work

Business As Usual (1981) #3
No Data.
10) Mr. Big

Hey Man (1996) #1
No Data. (It appears To Be With You didn’t chart, something that’s really bizarre because this band was really big in Japan.)
11) Mr. Mister

Welcome To The Real World (1985) #17
No Data.
12) Quiet Riot

Even though I couldn’t find something particular, the band had success in Japan, since their first two albums released there exclusively, and they did some live shows in Japan as well.
13) Rage

No info about charting positions, but the band was fairly popular in Japan during the 90s especially.
14) Rainbow

Down To Earth (1979) #90
No Data.
15) Scorpions

Crazy World (1990) #39
No Data.
16) Skid Row (US)

Slave To The Grind (1991) #3
No Data.
17) Supertramp

Breakfast In America (1979) #2
No Data.
18. Survivor

No Data.
Eye Of The Tiger (1982) #1
19) Toto

Isolation (1984) #2
2 Hearts (1992) #1
20) Whitesnake 
Whitesnake (1987) #19
No Data.
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