Tipped Arrows are a neat addition to combat within Minecraft, and can be used to apply status effects from afar. This guide goes over some of the more useful effects so that you know what to aim for.
1. Instant Harming
Instant Harming is an effect that, when applied to an arrow, will apply extra damage to its victim. The way Minecraft handles this is fairly strange, as it will check the damage the arrow itself has dealt, and if it has dealt less than 12 damage, will add Instant Harming damage up to meet 12. Instant Harming is a great way to deal with armored, non-undead threats, mainly players.
2. Poison
Poison arrows are slower to apply damage than Instant Harming, but can generally deal more damage. As such, Poison arrows are a fantastic option for consistant damage over time against mobs or players, assuming they are vulnerable to the effect. Unlike Instant Harming, there is no cap to the damage, so it can be used in conjunction with enchanted bows for maximum effect. Longer duration poison is recommended for tipped arrows.
3. Instant Healing
While it may seem counter-intuitive to place healing potions on an arrow, it can be a useful tool against the undead, since it will act in a similar fashion to Harming potions against them. Additionally, it can be used as a (albeit extremely hazardous) ranged healing option if you're accurate enough and your bow won't deal enough damage to kill your target, as the healing is applied after the damage of the arrow is dealt.
4. Slowness
Crowd control is an extremely important aspect of combat, especially when fighting other players. Slowness may not deal damage, but it will cripple the movement of your target, making follow-up shots easier. You can choose between extended duration or a higher level of slowness to really keep them locked down. It all depends on your preference and the situation at hand.
5. Weakness
Weakness, another crowd control ability, will remove the damage of the target upon hitting them. This can be crucial if you're planning on closing the distance for swordfighting, and will instantly put your target at a disadvantage on damage output. It can be applied semi-safely at range, giving you the opportunity to close in for the kill on your helpless prey. Just remember, Weakness itself does not damage your target.