<p>I found an article on getting active tcp/udp connections on a machine.</p>

<p><a href="http://www.codeproject.com/KB/IP/iphlpapi.aspx" rel="nofollow noreferrer">http://www.codeproject.com/KB/IP/iphlpapi.aspx</a></p>

<p>My issue however is I need to be able to determine active connections remotely - to see if a particular port is running or listening without tampering with the machine.</p>

<p>Is this possible?</p>

<p>Doesn't seem like it natively, otherwise it could pose a security issue. The alternative would be to query a remoting service which could then make the necessary calls on the local machine.</p>

<p>Any thoughts?</p>

There is no way to know which ports are open without the remote computer knowing it.  But you can determine the information without the program running on the port knowing it (i.e. without interfering with the program).
Use SYN scanning:
To establish a connection, TCP uses a three-way handshake.  This can be exploited to find out if a port is open or not without the program knowing.
The handshake works as follows:
The client performs an active open by sending a SYN to the server.
The server replies with a SYN-ACK.
Normally, the client sends an ACK back to the server.  But this step is skipped.
SYN scan is the most popular form of
  TCP scanning. Rather than use the
  operating system's network functions,
  the port scanner generates raw IP
  packets itself, and monitors for
  responses. This scan type is also
  known as "half-open scanning", because
  it never actually opens a full TCP
  connection. The port scanner generates
  a SYN packet. If the target port is
  open, it will respond with a SYN-ACK
  packet. The scanner host responds with
  a RST packet, closing the connection
  before the handshake is completed.
The use of raw networking has several
  advantages, giving the scanner full
  control of the packets sent and the
  timeout for responses, and allowing
  detailed reporting of the responses.
  There is debate over which scan is
  less intrusive on the target host. SYN
  scan has the advantage that the
  individual services never actually
  receive a connection while some
  services can be crashed with a connect
  scan. However, the RST during the
  handshake can cause problems for some
  network stacks, particularly simple
  devices like printers. There are no
  conclusive arguments either way.
Source Wikipedia
As is mentioned below, I think
nmap
can do SYN scanning.
Using sockets for TCP port scanning:
One way to determine which ports are open is to open a socket to that port.  Or to a different port which finds out the information for you like you mentioned.
For example from command prompt or a terminal:
```
```
telnet google.com 80
```
```
UDP Port scanning:
if a UDP packet is sent to a port that is not open, the system will respond with an ICMP port unreachable message. You can use this method to determine if a port is open or close.  But the receiving program will know.