I do not have this machine but my aunt does.
Check out the Threading diagram below, also shows some bobbin information.
Check to make sure there are no threads in your bobbin case area. The tension setting may be too loose.
Watch your thread it may be catching on the spool holder or maybe a burr or slit in spool catching causing needles to break. Check for burrs around needle plate or on the needles you ar using.
Make sure your using the proper needles.
Match the needle with type of fabric your using.
If sewing a knit you probably need a ballpoint needle...
Thread should be checked if old, it may have bad spots.
Make sure you pull threads to back of machine.
Threading make sure your thread is seated in all threading guides.
Before starting to sew pull hand wheel forward so needle is in fabric (needle down position).
Usually needles breaking the machine may not be threaded correctly.
If you have tried all the above may need to have it serviced. Might be a timing or belt issue. HTH

Here is a link that might be useful: Threading diagram

After you've tried all the things Pattie suggested, then check your upper thread tension. The bobbin and upper threads should meet in the middle of the fabric. If the upper tension is too loose it will put loops on the bottom of the fabric.

Before you touch the tension though make sure the feed dogs are fully up so it pushes the fabric along.

Myrna, Your right overlooked those tips ...

Make sure your presser foot is up when threading and down when starting to sew......

have a Singer Touch and Sew 603E, with the bobbin the winds in the machine. I ordered a new manual, etc. However. all the instructions to wind the bobbin say to push the wind bobbin button on the front of the machine. Mine does not have that. HOW DO I WIND THE BOBBIN? The manual does not give any other ideas except to push the wind button? Help?

If you do not have that button it makes sense to me that your bobbin does not wind in the machine. I don't know anything about your machine--this is just my common sense talking. You will not get much attention tacking on to an old thread. Make one of your own.

Where did the old bobbins go? I have old machines with the original bobbins and I still have them.

Anyways, the bobbins need to be for your model. If you bought bobbins for new Singers, they won't work right. You can find the right ones on Ebay.

the bobbins were drop in bobbins just wore out . Bought singer bobbins for the machine I have. At least that is what it said on the package. I can find other bobbins besides the ones that I bought at the singer place on ebay? Repair man seems to think that it skipped time. Sure wasn't doing it when I still had one of the old bobbins.

I've never had a bobbin wear out before and I don't believe it's normal. I have to wonder if something was wrong for them to wear out to begin with, which is what was wearing them out. They probably adjusted to the machine. Then when you got the new ones, you finally noticed the problem.

I think it's well worth it to get it fixed. They're good machines.

I have my mom's 600E from 1964 and never wore out any bobbins either,

I think that rattling around in the drawer may have nicked the edges and then the thread would catch. I have had this machine since the 80's. You are right it is a great machine thanks. I just thought that the new bobbins were maybe a little smaller or maybe thicker. I will have it looked at and know soon enough. thanks for your help

I have a touch and sew 603. My bobbin thread tangles on the reel latch and causes “bird nests” each time I sew. Any suggestions?