This can be hard to say for sure, so don't take the following as definitely proven. However, according to the C/Net website, tests measuring talk time found the Motorola Droid Razr Maxx to last longest with a total time of just under 20 hours. This was some distance ahead of the LG Optimus Vu, which reached just over 16 hours. You can see the full Top 20 list here (It was compiled in November 2012 so you can assume it's up to date).
In the future, though, it is hoped that the more or less daily charging of your mobile battery (which applies even to the best batteries if you have the phone on all the time) could be a thing of the past. Current research into fuel cell and other technologies looks as though we could soon be charging our phones and other appliances only once a month - you can learn more about this here.