Why can't I send a text message to someone in Switzerland or Holland?

From the US, you should use dial 011, plus the country code (31 or 41), and definitely drop the zero at the beginning of their number (if they gave one).
Good luck.

I don’t know why you can’t send messages, but I can try to give you two possible reasons why it could fail, in general: (1) instead of the ”+” sign you can try to use “00”, and (2) Dutch cellphone numbers start with “06”; leave out the “0”.
It would read like this then: 00612345678 (instead of 000612345678—or +0612345678).

Oh hey it works!
Thanks guys! :D

@rebbel
Sorry, mate you made a mistake, there. You left out the country code.

Dutch cell phone# 06 1234 5678 translates into +31 6 1234 5678. Or, dependent on your provider into international access code followed by 31 61234 5678.

Yup, @whitenoise, you are right, I did make a mistake…
Stupid, stupid, stupid, especially when you keep in mind that I was really thinking this over to give a sound answer :-)
Thanks!