Q: What's a good SSH Server that will run in Windows Server 2003? Disclaimer: I'm a little dumb when it comes to SSH.
I tried using openssh, but couldn't get it running properly, and MobaSSH would refuse my connection attempts.
What I really want is an ssh server so that I can back up a linux box using rsync. (Don't ask why I'm backing up a linux box to a windows box)

A: What is a good SSH server to use on Windows?
SSH / SCP Server on Windows

A: I have been evaluating KpyM SSH Server and it looks pretty good and is BSD-licensed with source. It is based on cryptlib fundementally and creates a Window Station for each session which is why it is one of the few open source SSH solutions that works correctly with PowerShell.
We have been using OpenSSH compiled for Interix/SFU/SUA for the last several years. The downside is that OpenSSH doesn't play all that nicely with PowerShell which is an annoyance and it requires the full POSIX subsystem from Services for Unix 3.5 or the Subsystem for Unix Applications (Win2k3 R2 and later). 
Years ago we used to use Vandyke and it worked well.
Follow-up on my look at KpyM SSH:
KpyM SSH is quite basic. One annoyance is that despite being open source it is nagware tat asks you to pay for a license key. It is easy to download the source, remove the nage and recompile, though. In general this is a basic ssh daemon. The best feature is that powershell works flawlessly. The configuration of KpyM SSH is pretty spare and the default encryption algorithms don't include aes128-cbc (aes256 is unsupported). If you start using TCP port-forwarding, your session says "entering port forwarding mode" and you can't interact with it anymore. You effectievly have to have a session for interactive commands and a separate one for forwarding traffic. It uses Windows authentication but doesn't support limiting access via Windows groups. Doesn't support public key logon. Does support granular access, sub-protocol (like offering sftp but not shell access) and environment control by account.
I like Bitvise WinSSHD much better.
Bitvise WinSSHD is much more impressive. Supports aes256 and aes128 out of the box. It is not open source but it is free (with AD integration crippled) for personal use and very reasonable $100 USD per server for commercial use. Can be configured to use powershell as the default shell and powershell works correctly. WinSSHD has very granular configuration per-account and per-group and per client IP and per client DNS. There are logon and logoff actions that can be configured per account or group. Supports OpenSSH public key files. Exposes an automation API. Write logs to the Windows event log and/or text file. Still has a small and light service process.
