I read a lot of blogs stating you couldn't get a pre-paid SIM card in Japan. It's true that the big players (NTT Docomo, Softbank, AU) don't sell these anymore but turns out that there is still at least one way to do this.
A company called b-Mobile sells pre-paid SIM cards valid for 1 month (about $USD32) and 3 month (about $USD100) with 1GB of data each. Yes, I wonder if anyone goes with the 3 month option...
The cards don't support calls but they run on NTT Docomo's LTE, HSDPA, 3G networks and data coverage seems very good.
You can only get them from big retailers. In Osaka, that means BIC Camera in Namba or, in my case, Yodobashi Camera in Umeda. You also need to activate them in Japanese - with a Japanese mobile apparently. So it definitely helps if you speak Japanese, have a Japanese friend, or if you're super convincing, maybe you can persuade the sales person to do it for you. From what I could tell, the U300 SIM they used to offer in English, pre-activated 24 hours after mail order purchase is no longer on offer. :(
In my case, I've been running on a 1GB, 1 month MicroSIM for a week now and using SkypeIn for receiving incoming calls. Calls are very high latency (almost unusable) but it has served its purpose so far - if I get a call that isn't working well, I just fall back to contact via email.
Best of luck Japanese travellers!