I actively follow the PSP Homebrew and hacking community. If you have any intentions of getting a PSP, DO NOT GET THE PSPgo. It absolutely sucks.
On a more hacking related note, most PSPs can run homebrew and custom firmware. Old PSPs like the PSP-1000 series and some of the older PSP-2000 models (with old motherboards) are able to run what is called permanent custom firmware. This involves modifying some of the PSPs flash data, and hence permanently writing the information to the PSP. This will permanently change your firmware and if you do this, don't use PSN. Ever. You'll get banned.
The newer PSP-2000s and PSP-3000s will need to run what is called temporary custom firmware. Due to increased security from Sony, hackers haven't been able to implement the same method of custom firmware as they have on old ones. Instead, an older exploit, the TIFF overflow exploit, has been brought back to create temporary custom firmware. By using a series of images, a PSP can temporarily boot into custom firmware. In this temporary firmware, homebrew can be run. What most people do is that they run a custom firmware installer. Of course, the firmware that is installed using this needs to be temporary too. But after installing the latest temp firmware (should only take a few minutes), ISOs can also be launched.
At the moment, the latest custom firmware is the Prometheus series created by a Chinese hacker. It is the only set of firmware able to run the most recent games without having to patch them first. It should be noted that there are many versions of Prometheus out.
5.50 Prometheus-2 is currently the latest version of permanent firmware. It is able to run games that require official firmware of up to 6.30, if I recall correctly. It requires you to have 5.50 Prometheus or 5.50 GEN-D before you can install it.
5.03 Prometheus-2 is the latest temporary firmware. You'll also need to download the image exploit known as ChickHEN to use it.
Finally, there is also a 5.00 M33 Prometheus-2, which is a permanent firmware for those people who never updated to the 5.50 GEN series and stayed with Team M33's latest release, 5.00 M33-6.
By the way, I recommend you check out the Monster Hunter series. It's the best selling PSP game in Japan. Monter Hunter Portable 2nd G (known as Monter Hunter Freedom Unite for NA/EU) sold over 3.5 million copies on it's first week of launch in Japan alone. Because of the success of the franchise (more recent entries to the franchise include the Wii's Monster Hunter Tri and PC/Xbox 360's Monster Hunter Frontier Online MMORPG), other companies like Square Enix and Bandai Namco have created their own 'clones', called Lord of Arcana and God Eater respectively. Despite being clones, they're still slightly different and are still fun.