I keep coming across patterns for things I'd like to make that require a serger, which I don't have (like patterns for cloth menstrual pads). Is there anything I can do with a regular sewing machine that would work instead of serging?
Check your machine manual for a section on overcasting. My machine has both an overedge stitch and something called a serging stitch. If yours doesn't have those, a regular zigzag stitch will work also.
Before I found my bargain steal $50 singer serger at the thrift shop I would turn and topstitch most things. It gives a neater appearance than just zig-zagging the edges. Also gives a smoother edge (more comfortable) for stuff like diaper leg holes and cloth menstrual pads.