As you might already know, there's 'homebrew' applications that you can get for your PS2. As there's quite a lot of these, I'm gonna briefly explain how to put a few on a DVD.
You WILL need a modchip or swap magic to play homebrew applications. You can find out information on swapmagic for both phat and slimline PS2s here.
First off, we need to make a file that tells the PS2 what to boot when it reads the disc. Open notepad, and copy this into it:
'BOOT.ELF' denotes what will boot. You MUST save this file as 'SYSTEM.CNF'
uLaunch Elf
If you need to create a disc with multiple programs on, you will need to use uLaunch Elf. uLaunch ELF will scan the DVD for other ELFs and allow you to boot them. Version 4.12 is attached, 'BOOT.ELF' is the only file in the archive that you really need. Download: View attachment 132685
Make sure you edit the SYSTEM.CNF file to boot this. For example, if uLaunchELF is called 'uLE.ELF', then change 'BOOT2 = cdrom0:BOOT.ELF;1' to 'BOOT2 = cdrom0:uLE.ELF;1' in SYSTEM.CNF.
uLaunchELF Official Forums (sign-up required) - Langauge packs and fonts - uLaunchELF release thread
Okay, so now you should have 'SYSTEM.CNF' and 'BOOT.ELF' (or whatever you've called it, aslong as SYSTEM.CNF points to it). So lets get some homebrew software!
SMS Media Player
From the title you can guess what this does, plays videos, music and probably other things. It's interface is very nice and simple. Unlike Reality Media Player Pro, this flawlessly played my 1500KB/S XviD rips of angel without skips. You can either drop the media files you want to play onto the same disc as SMS or drop them onto a seperate CD/DVD and swap the discs round. It'll scan the disc and show you a list of files, then choose what you want it to play. From there it's all fast forward, rewind, pause and stuff.
Snes Station
Snes station lets you almost flawlessly play SNES games on your PS2. The games I tried ran at full speed with nice sound. It also saves to your memory card. You can drop your *.SCM snes files into different directories if you wish.
PGEN
Emulates SEGA Genesis and Master System hardware at full speed with sound. Has a nice interface too.
You can also find many more homebrew applications for PS2 around the internet. I suggest you try PS2-Scene.org and PS2Dev.org.
Lets do it
Okay, so now you should have a bunch of *.ELF files, ROMs, MP3s or whatever you're planning to burn. Be aware that many applications let you switch discs. So what now? Time to burn it all.
First you need to compile an ISO, but you can't just burn em with Nero. You need a program called 'CD DVD-ROM Generator 2.0', you can download a copy here.
Using CD DVD-ROM Generator 2.0

Select 'Create New Project' and click 'OK'.

Now click 'DVD-ROM Master disc' and 'OK'.
Now click on the volume tab and fill in some information. It doesn't really matter what you type in here. Here's an example of what you could type:

Now click on the directory tab. It's important that you drag, in order, 'SYSTEM.CNF' first, then 'BOOT.ELF' (or whatever is the primary boot elf). Then followed by all your other ELF files, ROMs, media and whatnot. It's important that you fill up the DVD with ATLEAST 2GB, or you'll get a nice error screen. If you haven't got 2GB of stuff to put on, or just don't want to, you can make a dummy file using Dummy File Creator. Rename it's output to a *.bin file and drop it on.

Done? Now go to File>Export iml file. Save this anywhere you like.
Now open up IML2ISO, locate the IML file and click 'start'.

This'll take a while and look like it's crashed, but leave it.
Eventually it'll respond again, and you'll see an image file on your desktop. All that's left now is to burn 'n' play.
Have fun with all your ELF applications
Pre-loaded CD-Images:
SMS Media Player: CD Standalone or CD with SMS and uLaunchELF or Standalone DVD version