REN measures the load a device places on the telephone line when ringing.  A normal BT line will support a REN of at least 4, in other words at least a total of 4 phones/fax/modems should work on any line so long as their REN figures added together don't exceed 4.

You can quite often exceed this number because devices with a REN of 1 may actually have a real REN of only a fraction of 1.This is an anomaly of the test procedure used.  Moreover many lines can drive a REN of more than 4. 

Note that some elderly fax and answering machines can have very high REN's (and they really are high!).  If some or all of your phones fail to ring or some ring very anaemically then its possible you have exceeded the REN.  Try unplugging devices until they work.   You can get REN Boosters which will increase the ringing capacity of a line if desired.

Questions :

How do I know what REN my phones and other devices connected have ? - The REN will be displayed normally on the base of the device (near to the green approval sticker) or in the user manual to the device.

What devices don't have a REN ? - Generally speaking any device that is connected to your phone system that does not ring will not have a REN.  For example a caller display unit will have no REN nor will an alarm system that is connected to the phone line (the type that dial a number when the alarm system is activated).

Opps you just missed modems and answer machines from the bit above ! - No I haven't !, modem's do have a REN because they can be set-up to receive calls or fax's etc via your PC.  They have to respond to the ringing current in order to answer a call.  And also answer machines do tend to have a REN of 1.

What about a Sky Digital box that's connected to my phone line ? - A Sky Digital box has a REN value of 0.  It does not ring, and the software inside the box does not even look for a ring signal on the line.  If the manual to your Sky Digital box says it has a REN of 1, then you will normally find, in fact it is much less - 0.5, 0.25 even.  (its just to do with how the device was tested)

I've read this but I seem to think I have more than 4 REN but everything works ok, why is that ? - This maybe the case as for example a standard phone may say REN of 1 when it is much less.  For example I have a standard BT line and I have the following, and all devices work fine no problems.  2x Standard phones, 1x Cordless phone, SKY Digibox, Modem, Caller Display unit and answer machine.  You would think from that I have 7 devices that would be more than 4 REN, but remember my Sky box is 0 so is my caller display unit, the others say REN of 1 but are actually much less.

Can I increase the REN on my line ? - Yes you can buy what is known as a REN extender most will take you up to a REN of 8.  They tend to cost around £40 for a good one.

Each BT TwinTalk has a REN of 0.