Back to My Mac (iCloud)
If you're running Lion and have an iCloud account, you can use Back to My Mac. With Back to My Mac, your server will show up in the Finder's sidebar under Shared, just like it would if you were on the same local network.
This solution does not have a web interface, but I personally prefer connecting to my file servers the same way (through the Finder) whether I'm on the LAN or connecting remotely.
Slink
An alternative to iCloud that doesn't require Lion is Slink, which I highly recommend. I've been using Slink as an alternative to VPN for about a year without any problems.
Slink works similarly to VPN, connecting you to your network, not just your file server, but is extremely easy to setup (doesn't require entering a public IP anywhere). You setup your server by installing a System Preference pane (the Slink Agent), then setup the Slink app on each of the client computers.
Like Back to My Mac, this solution does not have a web interface. Also, like Back to My Mac, your server will show up in the Finder's sidebar once you've used Slink to make the connection.
You can purchase Slink from Slinkware directly or on the Mac App Store. They also have a demo available.
TeamViewer
TeamViewer is a common cross-platform solution for remote control and file sharing over the Internet, and it's free for personal use. It doesn't integrate with the Finder as Back to My Mac and Slink do, but being cross-platform definitely has its advantages. It also doesn't have web-based access, but there are TeamViewer clients for OS X, Windows, Linux, iOS, and Android, which may make up for it.
LogMeIn Pro
For a web-based solution, you could use LogMeIn Pro. Because it's web-based, it's also cross-platform, and there are client apps for iOS and Android. Unfortunately, the free version doesn't include file sharing.
You may also want to check out LogMeIn Hamachi, which functions more like Slink, but with more options. I haven't tried Hamachi in a long time, but when I tested it, it was less reliable and more difficult to setup than Slink, so I went with Slink instead.
My favourite swiss army knife for OS X, LaunchBar, has clipboard history and management. In addition to being able to access historical, clipped information it can also do clip-merge. A quick double press of Cmd-C will merge the currently selected contents in to the current top-of-the-heap clipboard object for you, allowing you to paste them as one object with a single Cmd-V.
You can merge multiple items in the clipboard history by selecting the first one and doing Cmd-C and then selecting additional items and doing the quick, double press of Cmd-C. They'll all get merged in to the top item as expected.
Best Answer
I use Copyclip. It remembers a certain amount of clips. You can also blacklist apps from which it should not clip something, for instance password managers. It does not use any kind of cloud. It is only local.
To verify that it does not use any cloud services. You can block the app from accessing the internet. OS X Firewall or third party app. Or you can check all established internet connections with:
Or trust the developers that they have not put any hidden cloud abilities into the app. Or use some OpenSource app and check the code. Or develop yourself.