When we started our company we have implemented Small Business Server 2003 on our (back then) only server.
Now we have grown, and the server is old and should be removed.
I would like to upgrade our network to a "normal" network.
The main reason for choosing SBS was the Exchange POP3 connector. We do not use that anymore, so we don't have a need for SBS.
What are the problems that I can expect? Or is this a normal, simple operation?
Sam beat me to this, as his answer came whilst I was typing mine. As Sam recommended, I will point you to the transition pack, from Microsoft. This knowledge article can also be very helpful, as well as this post, from which I quote one entry:
Bottom line, I do not see any major problems on a migration from SBS 2003 to 'regular' Windows Server 2003.
Unless you now require more than 75 licenses (the maximum allowed for SBS) then upgrading away from SBS will simply cost you more money for less features and will be harder to manage. Your stated reason for using SBS was the POP3 connector, but in fact that is an awful reason to use SBS anyway, since email delivery is much more appropriately handled by SMTP directly to your exchange server (the POP3 connector has its issues and was intended as a temporary migration strategy).
My recommendation: staty with SBS. You can still add additional member servers to an SBS network if that is your only concern.
If, even after this advice, you still feel that you need to migrate away from SBS, then the transition pack is your best bet as that's the cheapest way to get your additional licenses. You'll need to DCPromo another server and transfer the 5 FSMO roles to the new server, the Small Business Server can then be DCPromo'd off the domain.
It really depends how you want to do it. You can get the transition pack from Microsoft that will convert your licences from SBS to single components and remove the 75 user limit of SBS, you could then move this to a new server.
Alternatively you can install a new DC and Exchange server and move your users and data across, usually quite a smooth process. However, there are some problems, as stated here the FSMO roles are restricted to running on the SBS server. If you were to use the transition pack I believe you could then move them, but if you are adding just a new DC to the domain, you won't be able to move them from the SBS server, quite a big issue.
I'm also not sure how SBS will function if you try to add another Exchange server to the Exchange organisation.
My feeling is that the best bet is to get the transition pack, you will then have what is essentially the separate components of SBS, you can then look at adding new servers, transferring roles and turning of the SBS server.