All except the ones that reseed like they're going to take over the world - like Sweet Annie and Salvia sclarea (which is not an annual anyway) - OTOH, Sweet Annie smells so good I have a hard time yanking it!

This year I left all the red orach (Atriplex hortensis 'Rubra') seedlings to come up in my otherwise sparse blue/purple border. They made stunning 8 foot plants, but the ones at the front completely dominated the border. It looked a bit crazy, but it was fun. Next year I'll pull out the ones that are in the wrong place.

I let my volunteers stay wherever they sprout. The only ones I move are Cypress Vine. I remove unwanted morning glories. But my salvias? Wherever they pop up, they stay. I had a bunch reseed in a relatively new path, covered with fabric and with mulch laid atop. I have about 7 salvias, most relatively small, but I refuse to move them ;)

With the exception of purple Perilla, I love all my re-seeders. I am eradicating Perilla this year and probably next year too.