I have been experimenting with playing PS1 games on the PSP, and so far it has been a joy. For times when I am away from a PS2 console, having a portable console that allows me to play a perfectly emulated Vagrant Story anywhere was something I didn't think possible and yet I was doing so yesterday in the tube. Obviously you will need to install a custom firmware (3.40 OE-A and above) on your PSP which can be tricky but not too difficult, as well as access to a couple of PS1 games. As for the games itself, thankfully it is just about hitting your local independent video games store, flea market, GameStation, CEX or worse eBay. Prices varies based on quality and rarity, but you can never go wrong with a preowned classic like Metal Gear Solid for £2.99 (GameStation price).
Vagrant Story in zoom screen mode where the top and bottom part are cropped
Once you have ripped your game to your PC, you will need to a program to convert your PS1 game to a PSP format, in which case a PS1->PSP application like IceTea is needed. IceTea, for example, allows you to select the compression level. Using the 'best compression' setting, I was able to get Vagrant Story's 700MB ISO size down to 116MB file size, which is impressive as the game contains bits of FMV. You can also create your custom icons (144x80 PNG) and background image (480x272 PNG) for when highlighting the game file in XMB. Dump the generated Eboot file into a folder inside the ms/PSP/GAME folder on your Memory Stick. PS1 game saves will automatically created upon booting the game and you can manage it on the XMB save utility just like normal PSP game saves.
And here it is in normal mode which contains no cropping. Sorry about the crap lighting.
PS1 games can be played via different screen modes, including original and zoomed (both 4:3), zoom (cropped) as well as fullscreen (squashed). Because of the lack of dual analog as well as L2 and R2 shoulder buttons on the PSP, you may find some games to be pretty difficult to play. Fortunately there aren't that many games that uses those buttons or the right analog nub (Metal Gear Solid for example does not use the right stick). Plus you can map the left analog nub to emulate the L2 and R2 triggers. In Vagrant Story's case, the game actually support for the right analog stick for freelook but fortunately Squaresoft also mapped the same function to the Start key. Performance wise, the game runs brilliantly with no stuttering framerates or sound issues.
Hope this mini-guide will help. I tried to keep technical stuff out, but seriously, converting a game is a very easy process. Now if you excuse me, I need to go hunting for a copy of the super rare PS1 port of Chrono Trigger.