My most important features:
Optimization - so it would take less time and internet resources;
User Interface(UI) - smooth, easy to find stuff, fast and nice design;
Page saving - so you can save useful information and see it when you are offline;
Updates - so it would be updated in some time;
Buttons - at the bottom side of screen, so I would need to go anywhere. Buttons like tabs, refresh/stop, adress bar.
Video playback - so it would play video and didn't open a video application;
Download manager - so I would see how long does it take to download;
Speed dial - a homescreen to my favourite pages(I hope i'm right);
Pre-loaded - If I'm in a page's subsection and I go back to where I came, I would like it to not load the page again(I hope you can understand what I mean);
Sorry for my english.