There are other kernels like Liquorix that claim to be better optimized for desktop performance.
Though not recommended by some, you can often run official kernels from later versions of Ubuntu without issues.
(note that I haven't checked that one thoroughly so be wary as kernels are dangerous beasts) None of the above answers satisfied my problem of manually update the kernel to the latest stable version.
four warning signs of dating abuse - Updating linux kernel
Simply download the Ubuntu Mainline Kernel Updater script and run it from a terminal.
It will download the .deb's for you, install the new kernel, and optionally remove the old one (not recommended) then optionally reboot.
I'm currently running the 3.3.3 precise kernel on oneiric and my machine works better than ever.
Performance & battery life increased, while temperatures dropped a few degrees.
Thus I remove it's battery and rebooted and typed the command.