What are the pros and cons of using an exchange server thats hosted outside the company?

Cost and cost. And control over the server itself. However if you are with a reliable and legit facility that's generally a non-issue.

First and foremost, exchange is designed as a product to be hosted in-house.

Some of the functionality depends on protocols you may not wish to expose outside of your firewall.

Having said that, the product requires heavy resources and is complex to administer. Some organisations find that they need to use hosted exchange because they do not wish to make the investment.

I agree with @plumsauce that Exchange is primarily designed for internal use given some of its dependencies however given Microsoft's shift to promote online services I think it's best to say that this is a product that can be successfully hosted and consumed by an external hosting provider. For example: Intermedia is one of the biggest exchange hosting providers.

First and foremost, exchange is designed as a product to be hosted in-house.

Some of the functionality depends on protocols you may not wish to expose outside of your firewall.

Having said that, the product requires heavy resources and is complex to administer. Some organisations find that they need to use hosted exchange because they do not wish to make the investment.

I disagree. Every version since 2003 has improved functionality and performance on the WAN side. Everything can and will run just as well with a hosted version. The only thing you may notice is speed.

For example, setting up a new computer for an existing user with say a 1.5 GB mailbox... The new computer will need to download all 1.5GB of mail. This will obviously take much longer over the Internet than via your local LAN.

Generally speaking, your Exchange deployment is better off in a data center with stable power and cooling. Many office buildings (at least for the SMB) do not have "real" data center infrastructures.

My business isn't hosting exchange, but we do have several dedicated boxes that run exchange for customers outside our network. We have had no complaints.

What are the pros and cons of using an exchange server thats hosted outside the company?

Pros: if you do it right, you lose responsibility for the hardware and the uptime. Too, you might be able to get monitoring/support, if you go with the right provider.

Cons: It's more up-front cost to pay for someone else to manage your server. Lost direct access to the hardware (though you should still have remote administrator access, unless you go for a shared solution).

Exchange is designed for corporate inhouse those who need lots of feature, then these feature are copied by other Mail server developer. It an equation, more feature, more administration, more cost. Any other Mail server that providers same feature as exchange will also cost you. Comparison in terms of Feature then Exchange rules.

I do like the OWA feature that exchange has and with the OCS Wave 14 coming out, I think for large companies this will be a "wave of the future".