Overdrive just announced the release of the latest version of the Overdrive Media Console. With this update, you cna now check out and read Epub ebooks from your local library.
BTW, according to one poster over at Mobileread, the Epub downloads actually went live several hours ago. I guess they thought no one would notice.
You can find the iPhone app in iTunes and you can download the Android app in the Marketplace or direct fromOverdrive.

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OverDrive app for Android, iOS adds support for ePUB books from public libraries // Dec 7, 2010 at 6:10 pm
[...] The Digital Reader #gallery-1 { margin: auto; } #gallery-1 .gallery-item { float: left; margin-top: 10px; [...]
Big news! Our eBooks now have a smartphone app! | CADL Weblog // Dec 9, 2010 at 4:10 pm
[...] came early for our patrons who love the library’s Digital Downloads this year! It was announced this week that OverDrive’s (our download service provider) much-anticipated smartphone and [...]
OMC also does PDF FWIW.
A couple of problems (on iOS at least): it does not as far as I can tell, have a ‘return’ option to return a book early and let someone else borrow it. You would need to use ADE or something else (Bluefire for example) in order to do this.
The reader is too basic, no landscape, page transitions are a little jarring, and the navigation UI doesn’t autohide as one has come to expect. So I will use Bluefire, thank you very much.
The only problem with using the latter is than when you download with mobile Safari from your library’s Overdrive portal, the only target is OMC. So to get library content into BF you have to download to computer and move it over some other way (I think an alternate browser can be made to work around this but I haven’t worked out the details yet).