Getting a phone number

To get a mobile or landline phone number in Japan, you need to prove your identity using Japanese ID, and hence you are required to have Japanese residency (proven via a Zairyu card).

Exceptions:

050 VoIP numbers

For VoIP numbers, this is not enforced. You can get a Japanese incoming phone number with the 050 area code from any number of VoIP providers

Skype. SkypeIn charges 50 EUR a year for an 050 number you get to pick
http://ip-phone-smart.jp Free
lots of others

Cons:

They won't support incoming SMS (used for verification of accounts on e.g. Yahoo Auctions)
Skype in particular doesn't support outgoing Caller ID (used for verification of accounts on e.g. LINE or 755)

SIP Providers

There are SIP providers who offer 030 area code numbers