Why is it in Minecraft that every time you add a mod you get on but as soon as you open the world it crashes?

You need to make sure you delete the Meta-Inf folder.

Some mods are not compatible with other mods. This happens when both mods have modifications to the same .class file.

There should usually be a list of incompatible mods in the official forum post. If not, disable your mods one by one to determine which ones are not compatible, then report the issue to the developer of those incompatible mods.

Another reason is because some mods must be installed in a specific order.

For example, if you want to use "Too Many Items", "Single Player Commands" and "Zombes Modpack", the three most popular mods, they have to be installed in this order:

- Zombes Modpack

- Too Many Items

- Single Player Commands

Usually the developers will let you know if mods must be installed in a specific order to not crash.