What program do you use to create an abstract video?

For normal videos I would use Adobe Premiere Pro to edit it, but I don't see how you can make abstract videos with it.  I would do it with Macromedia Flash, but when I look at the galleries on this website the videos don't look like they were made in flash.

I mean the videos with a few line flowing over the screen. And some dots coming and dissapearing etc.

I don't have any experience in videos, but I do know that there would definetly be a program designed to do this. Maybe if you did a Google search for 'Abstract Video Tutorial' or something along those lines, it would have someone explaining exactly how to do it.

Here's a starter list. :) Google on these ones and you'll be good to go. I think Adobe After Effects is a good starting point, there's a lot of support and a big selection of plugins.

Video Production:
Adobe After Effects
 - Boris FX, Boris AE - After effects plugins
 - DigiEffects - After Effects
 - Walker Effects - After Effects plugins
 - Atomic Power -After Effects plugins.
 - Cult Effects After Effects plug-ins.
Eyeon Digital Fusion
Ultimatte Corporation
Video SpiceRack
Apple Shake
Hollywood FX 3D

VJ Mixing:
ArKaos VJ
AVmixer Pro
Elektronika
FFRend
Flowmotion
Grid Pro
Hex Patch running on Max/Jitter runtime
Isadora
Livid Union
Maxedia
modul8
motion dive tokyo
NeonV2
OpenTZT
Pilgrim Pro3D
Resolume
vdmx 5
Veejay
VIP 5.0
virtual dj
Visualjockey Gold
VJamm Blueprint
VJamm Pro
VJamm SE

Thank you for this huge list. I dont know that there are  many  softwares which are doing this. I know only Adobe for that!!!!

:)

Apple shake is the only program that I have experience in and feel comfortable using.

What is the mixing software for exactly?

I've only used the built in Mac editing software (iMovie I believe) and it worked well for my purposes. You could probably end up with a good abstract video just through filtering and editing. It takes more work on your end but it's more of a pure creative process.