Actually, it's not that I need a replacement for qmail, I already found one: Postfix. I need a replacement for the rest of the email stack, that works well with Postfix. My current setup constists of qmail, vpopmail, qmailadmin, and few others.
The stack should be able to handle a lot of email for a few hundreds of virtual domains. Email accounts for the virtual domains have to be managed through the web (adding new accounts, forwards, mailing lists, etc), but adding new virtual domains can be done in CLI. Of course, there should be a POP and IMAP server, and some antispam protection.
So, what software do you guys use in the wild together with Postfix?
Rather than trying to weld all that together yourself it might be worth considering something like Zimbra or Scalix, both of which do all the above out of the box and have open-source or "community" editions that are free from financial costs if that is a concern.
I run two small-scale Zimbra servers (one for myself and family+friends and one for a small office), in both cases the F/OSS edition, and find it far more practical than putting a stack together myself (even though I could if I particularly wanted to). As well as the POP and IMAP interfaces you get a rather good web based interface too which I use almost exclusively (though you can mix and match, one of my friends uses IMAP for quick checks on her iPhone when mobile and POP for downloading to her local mail store at home) - I'm guessing that the web interface with Scalix is not dissimilar. Provisioning domains and accounts can be done from both the web interface and the command line, though to get delegated administration (having different admin users for different domains or sets of domains) you need to pay for one of the supported versions.
As for scale, you need a more precise idea than just "a lot" when sizing up the capabilities of a mail stack. Do you have any approximate figures for what scale of data is stored and turned around by your current arrangement? The scale of your mail operation will dictate what sort of hardware are you are going to need to serve it too.