This article will give you a general overview of maximum number of email to send out per hour depending on your type of server or what you hosting provider permits.
Mail Policy and Limits
500 Hourly Maximum Outgoing Email Limit

This policy is applicable on a per domain basis on all Shared and Reseller servers, meaning that each addon and subdomain gets its own separate 500 outgoing emails per hour limit. This also applies to mailing lists. If a user sends over 500 emails in any hour, the emails will fail and may bounce back with an undeliverable error.

Each Connecting IP is Limited to 30 POP Checks per Hour

Users who attempt to go over the 30 check limit will likely get a password error indicating that the login is incorrect. The login error will subside within an hour and the email check will automatically unlock. The best way to prevent this occurrence is to disable email settings that automatically send and receive or set the email check to a higher time interval, such as checking once every 10 minutes.

Mailing Lists Over 900 Email Addresses Only Allowed During Off Peak Times

Any mailing list containing over 900 email addresses is only allowed to be sent during off-peak hours to prevent high server loads. HostGator defines off peak times as all day Saturday and Sunday, and 1AM - 8AM Eastern Standard Time, Monday through Friday.

Any mailing list larger than 5,000 email addresses will require a VPS or Dedicated Server. This means that users cannot send 12,000 emails a day (500 emails an hour x 24 hour period) on our Shared or Reseller plans. Please note that dividing one large list into smaller lists to get below this limit is not allowed on Shared or Reseller hosting plans.

If you receive a bounceback indicating that your email has been flagged as spam due to exceeding the 500 email per hour limit, wait until the next hour to continue sending emails.

Each Connecting IP is Limited to 30 POP Checks per Hour

Users who attempt to go over the 30 check limit will likely get a password error indicating that the login is incorrect. The login error will subside within an hour and the email check will automatically unlock. The best way to prevent this occurrence is to disable email settings that automatically send and receive or set the email check to a higher time interval, such as checking once every 10 minutes.

Mailing Lists Over 900 Email Addresses Only Allowed During Off Peak Times

Any mailing list containing over 900 email addresses is only allowed to be sent during off-peak hours to prevent high server loads. HostGator defines off peak times as all day Saturday and Sunday, and 1AM - 8AM Eastern Standard Time, Monday through Friday.

Any mailing list larger than 5,000 email addresses will require a VPS or Dedicated Server. This means that users cannot send 12,000 emails a day (500 emails an hour x 24 hour period) on our Shared or Reseller plans. Please note that dividing one large list into smaller lists to get below this limit is not allowed on Shared or Reseller hosting plans.

Limits

There is a 500 outgoing email hourly limit per domain. This limit is also applied towards Mailman. If you send over this amount in any hour, most of the e-mails will bounce back with an undeliverable error. If this occurs, it will then take some time for your account to be able to send again so we recommend waiting at least 1 hour after this issue occurs to begin sending email again.

Many of our servers have a limit of 30 POP3/IMAP checks per hour per each user's connecting IP address. If you go over this you're likely to get a wrong password error message or an error stating "login incorrect". If this occurs, please wait an hour and it will automatically unblock you. To prevent this from happening again, please make sure to disable auto checking or at least set it to something higher such as once every 10 minutes.

Any mailing list larger than 5,000 addresses will require a dedicated server or VPS hosting solution from us. Note: Dividing one large list into smaller lists to get below this limit is not allowed.

There is also a limit to the number of Mailman mailing lists permitted as follows (NOTE: This does not apply to other mailing list programs such as PHPList. This only applies to Mailman.)

Mailing Lists Rules

Any time you're sending a message no matter how large your e-mail list is you must throttle it. We recommend you throttle it to at the very least sending 1 email every 8 seconds. (Sending 1 every 8 seconds would send 450 emails within 1 hour, keeping you below the 500 outgoing email limit.) If the mailing list software you're using does not allow you to throttle you must switch to an application or script that will. We recommend PHPList, which can be found in your CPanel, under Quickinstall.

IMPORTANT: If you do not throttle and you try sending 500 emails, the server will try sending all 500 in 1 second which is not possible on our shared servers. This will cause a very high load on the server and the entire server will be sluggish, potentially affecting your sites and service, until this sending process is completed. It is our job to keep the server up and running without being sluggish or experiencing issues. Anyone who causes the server's load to go high will be suspended and the process will be terminated. If you choose not to throttle, you will most likely be suspended for crashing the server.

Any mailing list over 900 email addresses is only allowed to be sent to during off-peak times to prevent high server loads. Off peak times qualify as all day Saturday and Sunday, and 1AM - 8AM Eastern Standard Time, Monday through Friday.

The list must be a Double Opt-In list. This means a user has subscribed for a newsletter or other email marketing messages by explicitly requesting it and confirming the email address to be their own. Confirmation is usually done by responding to a notification/confirmation email sent to the email address the end user specified. The double opt-in method eliminates the chance of abuse where somebody submits someone else's email address without their knowledge and against their will. You will not be permitted to mail any mailing list that you were given or purchased. In doing so, this will also be considered spamming and may result in termination of the offending account.

Email Scripts must be able to handle and document all information from a double opt-in list. This includes recording the sign-up IP address and date/time, double opt-in verification IP address and date/time, processing opt-outs (via web or email), and list removal on bounce backs. All opt-outs or bounce back removals must be handled in a timely manner, and outbound mail must be throttled on shared packages to a maximum of five hundred (500) emails per hour. If your account is found to be using a script that does not meet these requirements, HostGator reserves the right to suspend, terminate, or deactivate your script or account.

Any unsolicited e-mail being sent will result in suspension or termination of the offending account. We take a zero tolerance stance against sending of unsolicited e-mail and other forms of spam.

Any mailling list MUST comply with all guidelines set forth by the United States government. These can be found at:
http://www.business.ftc.gov/documents/bus61-can-spam-act-compliance-guide-business.

No direct SMTP mailers are allowed. An example of this would be a Darkmailer or The Bat!. Any mail should be sent through the local mail server/MTA for further delivery by the server and not done directly by scripts.


VPS Plan and Dedicated Server Mail Limitations

HostGator's Dedicated Server and VPS accounts can send and receive unlimited emails per hour, and do not apply to the same mail restrictions listed in the section above for the Shared and reseller plans.

Our VPS and Dedicated server plans require that our users use a double opt in list or a safelist. For more information, please see the following article
Opt in mailing lists and Safelists


Email addresses on a single opt-in list are not confirmed. Anybody can submit anybody's address to the list, and it will be there until it is unsubscribed. This will be treated as spam.
On a double opt-in list, all email address must be confirmed before they are added. A request for confirmation is sent to the submitted address and the address owner must take some action to confirm that
she is the owner of the email address,
the address is working and
she indeed wants to subscribe.
Most often, the confirmation action is as simple as replying to the confirmation request or clicking on a link.



A safelist is a group of people who have agreed to receive emails from one another. Usually, the group requires membership and has rules regarding how often you are allowed to email the members.

CAN-SPAM Rules

All online businesses that use email marketing must follow and understand all of the CAN-SPAM rules listed below:

Message must be identifiable as an advertisement
Message must include an unsubscribe mechanism
Message must include a valid physical postal address.

Note: Deceptive subject lines and false headers are outlawed and taken very seriously. You will be held responsible if anyone sends emails on your behalf.

Open Relays

Open relays are mail daemons that allow mail to be sent without authentication to a valid local user. These relays are not allowed on HostGator services.

The Privacy and Electronic Communications Regulations 2003 cover the sending of email marketing. This legislation says that organizations must only send marketing emails to individuals if you have agreed to receive them, except where there is a clearly defined customer relationship.

Long story short: If you're sending email to people that never signed up for them, that you've not had a clearly established relationship with... it's spam, in its basic sense.

In addition, email servers connecting to Outlook must adhere to the following requirements:
Sender is expected to comply with all technical standards for the transmission of Internet email, as published by The Internet Society's Internet Engineering Task Force (IETF), including RFC 2821, RFC 2822, and others.
After given a numeric SMTP error response code between 500 and 599 (also known as a permanent non-delivery response), the sender must not attempt to retransmit that message to that recipient.
After multiple non-delivery responses (see #2), the sender must cease further attempts to send email to that recipient.
Sender must not open more than 500 simultaneous connections to Windows Live inbound email servers without making prior arrangements.
Messages must not be transmitted through insecure email relay or proxy servers.
The mechanism for unsubscribing, either from individual lists or all lists hosted by the sender, must be clearly documented and easy for recipients to find and use.
Connections from dynamic IP space may not be accepted.
Email servers must have valid reverse DNS records

With no certainty

I believe you can send as much as you want if you are not sending out spam emails

For example A boss who have a list of 10K Emails of people who works in his company if he had to send them all an emergent MASS email he should be able to ... No one of them will report this as a spam so he should be safe ( unless there are limits by his ISP )

But for someone who is trying brute force script to send emails ... or sending to a list of 10K emails who don't really want this email ( Sending ads or whatever ) you are spamming them they will report you and your IP will be blacklisted

You seriously expect someone here to tell you how to most efficiently spam people?