Mattress stitch (which is sometimes known as ladder stitch) creates an almost invisible seam, and I use this to sew most pieces of my knitted toys together.
Joining cast on and cast off edges
To join two cast off and cast on edges, lay the two pieces together right side facing outwards.
Bring the needle under the V shape of the stitch on one side. Then take the needle across to the other side and take under the V shape of the stitch.
Continue zigzagging across the work, pulling the seam closed as you sew.
Joining side edges
To join two edges of stocking stitch, lay the seams side by side, with the right side facing you. Thread a tapestry needle with a long length of yarn (at least 45 cm).
To sew the seam, take the needle from the front under the 2 “bars” (the horizontal strands of the rows above). Take the needle across to the other side and take the needle from the front under the two bars on that side.
Continue zigzagging between the two sides. As you sew, gently pull the stitches up to close the seam. Don’t pull too tightly, or the seam will pucker.