My house was built in 1940. The basement has a drain that comes out of the middle of the floor, and overflows whenever the washer is run and sometimes with flow from the kitchen sink and dishwasher on the main floor.
Is it safe to snake? Should a professional do it?

It should be OK. If you run water down this drain does it back up? Is there a cleanout you can open to check? It is always better to rod through a cleanout than a trap. If you do not have experience with a sewer machine I emphatically do not think it is a good idea for you to do it unsupervised. It is a very powerful machine that can do damage to you and your property, not even forgetting what happens if you get it stuck, or god forbid, you break it in the drain.

Thanks... husband got someone to come in and snake it and apparently the whole thing is solved. We'll see... :o

If it backs up within 6 months have the line snaked again then camare it. Tell them you want the video. Sometimes they forget to turn the sound off [grinz].