1. On long seams, such as a tent or tarp: if the thread has lower stretch than the fabric, i.e. polyester thread on nylon, a zigzag stitch will keep the thread from snapping when the stronger nylon fabric stretches. And it will prevent the thread from sawing against the fabric until one or the other fails. The zigsag does not have to be deep, just enough to give some slack when the long seams stretch.
2. Sailmakers use a zigzag - which is also called the "sailmakers' stitch" partly because sails are subject to a lot of wind shock causing the seams of bias cut fabric to stretch, and partly because it is easy to rip out zigzag stitches when a seam needs adjustment during manufacture as it often does.
3. If the thread has the same stretch as the fabric or more streth than the fabric, a straight stitch is stronger.
4. Consider whether the seams are square or on the bias. Even polyester sailcloth strethes when pulled on the bias. For bias seams, the stretch of nylon thread makes the seam stronger.
5. Tests reported on this site have shown that parallel lines of straight stitches are stronger for reinforcements in ultralight fabric than are zigzags or bar stitches.
6. Gear manufacturers (including sail makers) usually just learn from experience like everyone else and apply rules of thumb. In general outdoor gear, the tendency has been to use long stitches with strong, stretchy thread. It works and long stitches are easier to remove when (not 'if') a mistake is made. General purpose polyester thread is strong enough for almost all DIY projects except perhaps sails. Lightweight nylon upholstery thread is good for DIY sailmaking and when sewing heavier fabrics such as 10 oz or heavier Cordura.
7. Things get tricky with climbing gear because of shock loading versus static loading. Improper over-stitching can weaken webbing, for example. You just have to know. And test. Carefully.