As of today, homebrew is once again available on all PSP firmwares as another exploit is found in firmware 2.00, 2.01, 2.50, 2.60, 2.70, 2.71 and 2.80. Currently, there is no eLoader for this exploit, but with time, 2.00+ users can use this exploit instead of the GTA exploit. It also means that 2.80 users can also use homebrew although Kernel access will be denied. The exploit was discovered by NOPx86 and with the help of several others (psp250, skylark, joek2001, jimp, cswindle, and Fanjita) the exploit was transformed into something that can run code.
For firmware users of 2.00 to 2.71, Kernel access will be possible, however, 2.80 users will not have this luxury due to tighter security measures. Download the exploit here.