A number of applications have the handy feature of allowing users to respond to notification emails from the application. The responses are slurped back into the application.
Bose has a pretty great system where they embed a Queue and Ticket ID into the email itself.
My company has the traditional Case # on the subject line, but when CREATING a case, require a specific character string "New Case" "Tech Support Issue" on the subject line to get through the spam filters.
If the email doesn't match the create or update semantics, the autoresponder sends an email back to the recipient demonstrating how to properly send an email, or directs them to our forums or web support site.
It helps eliminate the spam issue, and yet is still accessible to a wide technical audience that is still heavily email dependent.
Email is a cesspool of bad standards and broken clients. You need to be prepared to accept almost anything as input. You will need to be very forgiving about what kinds of input are tolerated. Anything easy for you to program will likely be difficult for your users to use correctly. Consider the old mailing list programs that require you to issue commands in the subject line. Only hardcore nerds can use those effectively. And some of those trouble-ticket CRM things you mentioned have bizarre requirements, such as forcing the user to reply between two specific text markers in the text. That sort of thing is confusing to people.
You'll need to deal with email clients that send you formatted text instead of plain text. Some email clients still don't handle HTML properly (cough GMail) so your replies will also need to be designed appropriately. There are various ways in which photos might be "uploaded" via email as well, especially when mobile phones are involved. You will need to implement various hacks and heuristics to deal with these situations.
It's also entirely possible that you will get email that is valid but unusable by the email parsing library you are using. Whether or not this is important enough to roll your own will be a judgement call.
Finally, others have mentioned using specific email addresses to uniquely identify a "conversation". This is probably the easiest way to do this, as the content of the mail will often not survive a round trip to a client. Be prepared, however, to get mail to old IDs from old customers who, instead of opening a new ticket somehow, reply to an old ticket. Your application will probably need some way to push emails with an old ID into a new case, either manually or automatically. For a CRM system it's very likely that a user would reply to an old email even if you already sent him a new email with a new ID in it. As for whether you should use some.email.address+some.id@yourdomain.com or just some.id@yourdomain.com, I'd go with the latter because the plus-sign confuses some email clients. Make your IDs guids or something and have some way to validate them (such as a CRC or something) and you'll get less junk. Humans should never have to type in the GUIDs, just reply to them. The downside is spam filtering: a user's computer might view such email addresses as spam, and there wouldn't be an easy way to whitelist the addresses.
Which reminds me: sending email these days is full of pitfalls. There are many anti-spam technologies which make it extremely hard for you to send email to your customers. You will need to research all of these and you need to be careful, and do some testing, to ensure that you can reach the major email providers. A website like Campaign Monitor can help you if you are sending email.