1. Re-thread your machine, while making sure that you hold the thread very tight (it mustn't loop anywhere). Then, BEFORE stitching:
2. Verify that your thread cone sits steadily on the spool pin (especially if the holder is horizontal). Secure it using spool holders if necessary (these are the little plastic caps that come with each embroidery machine).
3. Ensure that the thread CAN'T wrap around the thread holder. If it wraps, it will DEFINITELY break.
4. Make sure that the thread doesn't catch on the spool edge. This problem often pops up when using small "mushroom" type thread spools (usually the 275-yard ones). After unwinding normally for a little while, the "mushroom" edge starts preventing the thread from going off the well, and the thread starts breaking. This is one of the reasons to use large thread cones, and not the small ones - large cones usually have a better shape.
If you already have some small spools and are determined to use them - try them with the vertical spool pin, and loosen top thread tension a bit. A separate vertical thread stand also helps thread to feed up better, and avoid it's friction with the plastic spool edge.
In case your machine doesn't have a vertical spool pin and you don't own a thread stand either - consider getting a kit with 1000-yard thread cones. Thread stands cost $50 - $100, and for that money you may get many good thread cones.
5. Check needle size, type & condition:
Check for any wear on the needle and replace as necessary.
80/12 needles usually work great with regular 40wt embroidery thread. For metallics or thick cotton thread, try using metallic needles. They have larger eyes, often coated with Teflon, to help thick thread move better.
6. Take thread end into your hands. Unwind a couple of meters and pass it between your fingers. It should be smooth and consistent, without knots. If it's not the case - try to unwind several more meters. Sometimes thread can be damaged only in a certain place on spool. If it's still inferior after you unwind several good meters - put that spool aside and take another one.
7. If none of the above helps, and you're SURE that the thread doesn't catch anywhere, try to lower top thread tension (your machine manual should have an instruction for adjusting thread tension).