Solder does not stick to iron after cleaning

No, absolutely not, flux is NOT optional. It is absolutely required. Your solder should have rosin flux in it.

Did your iron sit turned on without solder on the tip? That will cause a layer of hard corrosion to build up. Always put fresh solder on the tip after soldering, and before turning it off.

Iron cold: Clean the tip gently with a brillo pad. Wipe it clean with a paper towel.
Take some rosin core solder and wrap it around the tip.
You'll have to hold the iron at an angle, tip pointing up just a little to keep the solder from sliding off.
If you have some flux (DO NOT USE PLUMBERS OR ACID FLUX!), then add a little to the solder coil on the tip.
Turn the iron on, and stand ready with some more solder in your other hand.
When the solder starts melting, it should stick to the tip now. Add more solder as needed.

Extra flux is mandatory with lead-free solder. You may find you need to apply it to each joint before you solder.

I prefer not to buy my solder and flux from Radio Shack.

Let us know how this works out.