The usual reason is that the machine is misthreaded, or that there is a rough spot somewhere on the thread path, or you've got cheap thread. Here's the manual for your machine, assuming you've got a 2263 (621B does not look like a Singer model number):
http://www.singerco.com/uploads/download/1180_2263%28eng_spa_fre%29.pdf If you do have a different model, look for the manual here:
http://www.singerco.com/support/instruction-manuals
Take all the thread off of/out of the machine and clean it per the manual instructions. Put in a new needle, right way around and fully up in the needle clamp. Rethread from scratch, with the upper tension set to 3 and the presser foot raised while you are threading. (see also:
http://www.picturetrail.com/sfx/album/view/22521551 )
Make sure your thread isn't making extra loops around any of the points it passes through while threading, and is not catching on the spool or the storage notch that's on the bottom of some thread spools.
If that doesn't improve things, try again with a second new needle (the most common spot for a snag is the eye), and also wrap a piece of slick fabric around the pad of your index finger and pull it tight. Feel each eye the thread goes through, the presser foot (top and bottom), the needle plate (=throat plate), the sewing hook and bobbin case. If you find snaggly spots, they can be gently polished out with crocus cloth.
Oh yes, buy good thread. The cheapie stuff is normally just garbage.
http://sewing.about.com/library/weekly/aa102100a.htm