Some do and some don't. However, this information is only mentioned on
the Japanese pages e.g.

http://www.freespot.com/map/tenpo.php?n=3887
(Set you security settings to WEP and ask the staff for the key.)

The Sun Hotel in Wakayama mentioned above doesn't have any encryption
(or, at least, any mentioned). All you need to do is set you SSID to
"FREESPOT" and connect. No credentials from your ISP required. Of
course, if you can't connect without encryption then it's a pretty good
sign that encryption is required and you should approach the staff at
the location.

Cheers,

Scott