Most complex applications actually need to be installed on your new system, because they make registry keys and such that are required to execute properly. You can just try copying the folders to test it out, and just delete and reinstall the ones that don't work. As far as actually doing the transfer, if you have a desktop which has some room and a spare connection for the hard drive, you should be able to hook it up (though you might need to configure it as a 'slave' on the IDE chain. There's usually a small square jumper that you need to move to set it to be a slave, though you'll need to read the manual for your model hard drive to figure out where it needs to go. Here's some step-by-step instructions:
Installing a Hard Drive. Presumably you'd want your new system's drive to stay the master and set your old one up as the slave.
If you don't have a free slot to mount your new drive to the case, which is more common with smaller profile desktops, you might just need to leave it dangling while you transfer the information. Just make sure that the circuit board on the bottom isn't coming into contact with anything metal, and disconnect it when you're finished.
(Edit) Other options include: File sharing over a network (kinda slow if you have a huge amount of files) and USB crossover cables (they sell cables designed for data transfer)