Detergent gets too much credit and too much blame. Most stubborn stains are won or lost in the pretreat step, before the item ever goes in the wash — the detergent's job is finishing what the pretreatment started, not doing the whole job alone.
Grease and oil
Blot (don't rub) excess grease, then work a small amount of dish soap directly into the stain — dish soap is formulated to cut grease more aggressively than most laundry detergents. Let it sit for a few minutes before washing on the warmest setting the fabric allows.
Grass
Grass stains are protein and pigment combined, so cold water first matters — hot water can set the stain before you've treated it. Apply a stain pretreatment or a small amount of liquid detergent directly to the area, work it in, and let it sit 10–15 minutes before washing.
Red wine
Blot immediately, don't rub. Cover with salt or baking soda if you're not near a sink to absorb what you can, then rinse the back of the fabric with cold water to push the stain out rather than further in. A dedicated stain remover before washing improves the odds significantly over detergent alone.
Blood
Cold water only — heat sets protein-based stains like blood permanently. Rinse or soak in cold water first, then treat with a small amount of enzyme-based stain remover or detergent before washing.
The order that actually works
Identify the stain type, treat with cold or warm water accordingly (never hot, until after you're sure the stain is out), apply a targeted pretreatment or stain remover, let it sit, then wash. Skipping straight to "just throw more detergent in the wash" is the most common reason a stain sets permanently instead of coming out.
The bottom line
Keep a dedicated stain remover and a small bottle of dish soap near the laundry area, not just in the kitchen — between the two, most common household stains are treatable before they ever reach the wash cycle.