How to send Mass emails to humungous numbers

Hi guys

I have been collecting emails from my website visitors, who are interested to receive info, and I can say that I have collected a pretty large number of emails.

Now with my current web host (and pretty much most web hosts) I can only send 200 emails per hours. So usually to send a mass email, I send to the first 200 (and keep track of which email I stopped at), then after an hour send to the second 200 etc.

Is there a way or service that can help me send to all those emails at once?

Thank you!