A lot of time, I need to connect to my stand alone Windows 2003 server at datacenter with public wifi like wifi at starbucks. From my understanding that SSH to a Linux server through public wifi is safe but how about remote desktop with public wifi? Is it safe to remote desktop into my server with public wifi?
Thanks
RDP encrypts the communication channel so this is safe.
RDP'ing to your server is about as safe as SSH'ing to your server in that those particular channels are encrypted, but there is a possibility that your system can be poked and prodded through other means if it's a fake network made to capture traffic or take advantage of exploits. You should make sure it's firewalled and extra services are turned off; Windows especially seems to have a lot of automatic features made to make things easier and/or more convenient and can potentially cause problems.
VPN's would encrypt your traffic better if you can configure it to tunnel all your traffic, not just traffic to a particular route.
So in general yes it's safe enough for general use (practically speaking) but you're still open to other attacks and exploits by using an open wifi. Keep your system up to date, run AV software and malware detection and keep an eye on your logs.
RDP has some encryption of its own which is probably good enough for LAN use but I'd certainly hesitate to use it over the larger Internet, so if you're really worried about securing this traffic (and I would be) you can create a VPN using whatever tools you have to hand, establish the VPN connection then connect to your RDP session over the VPN. Or if you can update the server to windows 2008 my suggestion would be to use the Terminal Server Gateway role on a web-facing windows 2008 server to create a nicely wrapped up SSL VPN to protect your connection.