How to create custom borders like classic Atari Arcade flyers, in Illustrator

For my part you are welcome, Kapp.

Kapp,

For the asymmetrical paths in ATARI and ASTEROIDS, simple use of Art Brushes would seem an obvious choice as mentioned by John.

For the symmetrical paths in CENTIPEDE and POOLSHARK, you can use either Art Brushes or multiple Strokes, along with negative/inward Offset Path to get much of the shapes, with some afterwork including rounding, cutting/(re)joining, and copying (parts), and in CENTIPEDE an overlap of the yellow cenrtre band, and also Knockout Group based on a 0 Opacity outer part of the yellow(ish) path for POOLSHARK, to obtain (something close to) the appearances shown.

Below, you can see steps/layers in creating a crude Knockout Group sample corresponding to the top of the POOLSHARK.

Click Here to see in Chrome 

Each one of your samples are significantly different.  Each one would have its own approach.  Given that, you have a few different options at your disposal.  One is to create a brush using a segment of the border.  Then, create a rounded rectangle and apply the brush to that.  Those samples are each custom artwork.  I would print each one as large as you can using whatever printer you have available.  This will give you a chance to measure corner radius diameters to be applied throughout.  In your first sample. I would create the outside corner radius using the ellipse tool ( say one inch ) at around 12pt stroke, no fill.  Discard top anchor point and right anchor point, should leave you with a corner.  Select that segment and use Offset Path > experiement until you get the spacing you want > repeat for the third segment.  When you have the three corner segments done, select all > covert to paths.  You will now duplicate the three segments for each corner of your design ( if necessary ).  You can now extend the ends of the corner to reach its destination.  So, I have given you two ways to achieve the first sample: one using a brush, one creating the corner manually.  Again, each sample is considerably different.  You can also create a tracing Layer to help follow along the original artwork ( Place the image or artwork on a Layer, then create another Layer to use for your tracing ( artwork ).

Just to explain better what I've tried so far...

1. I will use line tool to just make the straight lines in varied colors
2. Bump up the stroke size to create "fat" lines
3. Use the Arc tool to create the curves... Stroke size and color matched
4. As can be seen in my example, these items are not one continuous line
5. ...the broken line can easily be seen

I feel like theres a way to create an arc and then just "stretch" the top and bottom of the arc out, and have those lines be at 90 degree angles to the artboard's corners...

THANKS ALL for any suggestions