I have a vanilla server, recently (excitedly) upgraded to 1.7.2 (did not run any snapshots since 1.6.4). Since then I have had problems connecting to my own server. So background and extra info:

I recently moved into a crappy area of Colorado (bandwidth speaking) and went from a decent 16Mbps to about a sad 1Mbps down and about 3Mbps to 1.5Mbps up (don't ask how that works) sort of situation.

This happened around Sept. 22nd, so from then on, no problems till the 1.7.2 update on Oct. 25th. On the 26th I MCEdited the world to delete chunks where no one had built. Uploaded the world back to the server same day as updated to 1.7.2, and was able to connect no problem. World seemed fine, everyone said the update went well their things were still there and was excited for the update.

I played a bit but nothing crazy and things seemed to be all right. Then I started getting disconnected. But not only would I get disconnected, the server would crash completely. Nothing in the error log, and I finally decided to run outside a screen and the only thing in the console was 'killed'

I'm on a digitalocean server with 1GB ram, 30GB SSD, and Ubuntu 12.04.

Since this has started happening, none of the other players have had an issue. So it seems to point to something about my network. I reduced my start script to the bare minimum:

screen -S minecraft java -Xmx610M -Xms512M -jar minecraft_server.jar

And still have the issue. I have used three computers on the same network all with the same problem. I recently took one machine and put it on a better network and had no problems.

At this point, most the time time I join for a few seconds and then disconnect and kill the server, albeit sometimes I can join and as long as I don't leave, I can stay connected for a couple days.

I switched back to 1.6.4 and don't seem to have any issues at all.

I tried upgrading my server to a 2GB ram and 64GB SSD (same start script) and still had the same problem when using 1.7.2.

When I'm on windows (7) the client disconnects with error message:
Internal Exception: java.io.IOException: An existing connection was forcibly closed by the remote host

On Mac OS 10.8.4 my error message is:
Internal Exception: java.io.IOException: Connection reset by peer

At this point I can honestly say I have tried absolutely everything I can think of, it's not a big deal for me as I will only have this problem for a couple months till I move to NY but I fear others (probably with slow internet/ping) may not be able to join in any multiplayer games. And it's scary that someone like me could attempt to join any server and completely crash it. Let me know if you want me to try, because so far I haven't, GGG and all.