Update: This post was written in late 2010, a time when it was difficult to find a PDF app for a cheap Android tablet. That is no longer true.
If you need a PDF app today, look in Google Play. If you can't access it, try the Amazon Appstore. If that is inaccessible then the apps mentioned below will tide you over until you find something better.
If you are reading this then you have probably found yourself in need of a PDF reading app. (If you're in a hurry, scroll down to the end.)
So did I, and after looking here and there I found a number of free PDF readers. In order to save myself some trouble next time around, I pulled together a list of 7 apps. All are free and can be downloaded from your web browser.
Is this every PDF reader? No. Just the ones I could find easily and link to.
I ended up getting the apps from only 2 sources. One is the SlideMe App Store and the other is Freeware Lovers. In total, I checked 7 sites. The other 5 had poorer selections and didn't have any app that I couldn't find at the first 2.
Update (29/5/2011): Amazon has launched their Appstore, so you might want to check there for free PDF Readers. I found Aldiko there, but it requires a later version of Android than i have on my Pandigital tablet.
If you can, you might want to look at the Android Market. I'm sure there are PDF apps in the Marketplace but since I can't access it I couldn't test them.
I was disappointed with all the apps. None of the apps had any annotation abilities, support for table of contents, or a zoom setting that cropped the white space. I was also surprised that only one had text search. I have a 6 year old version of Adobe Reader for WinCE that could meet or beat all of the abilities of all of these apps. That's pathetic.
Some apps I didn't test
Several of the office suites for Android include PDF viewers. If you have one then you might want to check it and see if it works for you. I also didn't test anything that I couldn't find outside of the Android Market. I'm sure there are PDF apps in the Marketplace but since I can't access it I couldn't test them.
Update: Kindle, Montano, Bluefire Reader for Android, and Aldiko can display DRM-free PDFs.
(SlideMe, v1.5+) Page turns and opening the file were reasonably fast. It has a go-to-page and zoom options, but it lacks reflow, search, and TOC support. Also, whenever I tried to zoom in, it crashed. (It's still under development). But it does have little on-screen page turn buttons in the bottom corners.
Update: The developer behind DroidReader left a comment about features he's planning to add.
Update 29/5/2011: It appears to be broken. I can't get it to open any PDFs.
(SlideMe, v1.5+) It doesn't do page turns, only scrolling. It has zoom, go-to-page, and text search options (this may not be working right) but no reflow or TOC support. I think this one would be good for a smaller screen (under 5"), but it was a waste on a 9" tablet. On a smaller screen the scrolling could be a useful feature.
Update 29/5/2011: This app has been updated since I reviewed it last, but it doesn't appear to have any new features.
Adobe Reader 9.0.2
(Android Freeware) Based on the ones I've tried, this was the best app if you have a large screen tablet. It only has the fit to page width option, but it also has text reflow. There's no search, page jump, or TOC support. But I like that you can either scroll or turn the page. This was also the only app to find my PDFs and list them without having to find them manually.
Adobe Reader 10.0
(Android Freeware) This couldn't install. It requires v2.1, unfortunately.
(Android Freeware) This is a basic app with only a page jump option, but no search, reflow, TOC support, zoom. You can scroll but not turn the page.
(Android Freeware) This is pretty much the same app as VuDroid. It only had a page jump option, but no search, reflow, TOC support, zoom. You can scroll but not turn the page.
All of the PDF readers were tested on a 9" Android tablet running v2.0 and the Spare Parts app. I couldn't find compatibility info on several apps so I don't know that they will work with earlier versions of Android. Also, some of these apps might require the Spare Parts app in order to display full screen on a large tablet so you might want to install it.