I use the paid version of ezPDF reader. It's 5 bucks or something . I'm a pretty basic user when it comes to reading, but it definitely remembers your position, has a decent search functionality, and allows me to make easy annotations as well as far more features than I use.

https://play.google.com/store/apps/details?id=udk.android.re...

For reading comics (another awesome use case for the tablet) I'm using Perfect Viewer:

https://play.google.com/store/apps/details?id=com.rookiestud...