Eagle will not finish auto routing?
Something that is inherently difficult can't be made easy.

A few tips to get better results, most are in the comments too:


place the components carefully. look at what the autorouter has produced, especially at the places where he had to take weird roues, or could not route at all, and think of a better way to arrange your components. Another way to approach this is to vieuw the ratsnet lines, imagine they are all elastic wires pulling at the components, and imagine where that would draw each component. BTW placing includes rotating and mirroring to the other side (if you want to allow that).
route the 'obvious' traces by hand, save your PCB, and then start the autorouter. you can route a trace whith the rest of the traces in mind, an autorouter is stupid and looks at one trace at a time. Even when I use the autorouter, I often first route the power and ground traces (and other high-current or noise-sensitive traces, if any) myself. That is a good moment to check the placement of your decoupling capacitors!
use a finer routing grid (as always, this is a trade-off: a finer grid has more routing opportunities, but also takes more time to autoroute)
use smaller via's, finer traces, smaller distances, more layers. but check with your PCB manufacturer!
use a bigger PCB so there is more room between the components for traces.
play with the autorouters settings, especially the cost of via's and the preferred direction on each layer. My experience (in hand routing) is that strictly keeping to (for instance) horizontal on the top and vertical on the bottom often gives better results in the end than making that shortcut to a nearby pad in the 'other' direction. (You can make such shortcuts after full routing to clean up the design.)
route yourself. even if you don't use the result, it will give you a better feeling for what the issues of routing are. (One of my sons (then 12y old) played routing with the concenration that he otherwise reserved for video games.)