Note from dev: this post is legacy. Some information might still be useful, but Obsidian for Mobile has been officially released as of 2021/07/12.
Obsidian will have a mobile version! But it does not, just yet. Here are some options for working around that.
Your notes in Obsidian are kept in markdown files, which are at base plain text. Therefore, you can edit them with any text editor, and if you sync to your mobile device with any cloud service you can edit them there.
That said, what you choose for that depends on your circumstances and requirements.
The most popular editors for iOS seem to be 1Writer and iA Writer. Both are well designed apps, with markdown editing at their core. 1Writer natively understands the linking and tag syntax that Obsidian uses, with the limitations that links to subfolders won’t work, neither will
[[piped|links]]. iA Writer has several features dedicated to prose writing, such as detecting parts of speech. So, both have their uses depending on what kind of work you are doing.
Some users report that iA Writer works better with Google Drive, and 1Writer works better with Dropbox, but I’ve not been able to test that.
[Edit 2020-05-27] We’ve also had a report that mdnotes (app store link) is a good choice for a free markdown editor.
iA Writer is also available for Android. Another popular option is Markor, some folks report that it is very good for rapid launching for quick note taking.