I?m building a DC circuit with 3 components. 
A small IC (integrated circuit), 1.8-5.5volts, which uses 2.2mA when
at 3 volts when active and <1 microAmps when a 'sleep'.
A sensor which needs to run at 4.5-5.5 volts and when active runs at
33ma (50ma max)
A transmitter which when running requires 20ma at 3 volts (can use 2-4 volts).

The whole project requires very low power consumption and a single battery source.
I had plans to use 4 x AA batteries (1.5volt x 4 = 6volts) and put a
small resistor between that and the sensor. This covers the sensor ok.
However I also need a to provide 3v (give or take a little) to the
transmitter and IC
However I don't know whether to use a regulator or resistors to do this.

My question is in the case above which will use the least power, the
regulator or resistor(s)?

Several points. First, when designing efficient battery powered
circuits, to extract most of the energy, with alkaline cells you have
to design to an end voltage of 1.0 volt. There is very little to be
gained lower than that. Bear in mind too that the initial voltage is
around 1.6 volts, which drops rapidly to a much more gentle slope. The
exact figures depend upon the load.

If you use a resistor rather than a regulator, the voltage which will
be supplied to the load will be extremely variable. Also several
resistors feeding different loads will impact upon each other in the
way that ?Don?t flush the toilet while I?m in the shower?. Basically,
unless the voltage requirement are very loose, resistors are unlikely
to be satisfactory.

Regulators do a good job of stabilising voltage, but most require well
over a volt across them to make them work. So you lose much of your
battery capacity before you start because to get 5 volts you would
need over 6 volts from your batteries to be safe. Low dropout
regulators are available though, which require only a tenth of a volt
or so across them so you?d get better battery utilisation. Check out
your favourite electronics supplier for suitable items.

However, the best way for efficiency is generally to use a switching
regulator. These can be over 90% efficient, though usually more in the
region of 75 -80% for small off-the-shelf switchers when used as
suggested. One advantage of a switcher is that you can generate
several voltages at any (within reason) voltage either up and / or
down. I shan?t go into the technicalities because it is a *huge*
subject. Nevertheless, with a handful of small components you could
generate all your voltages from a couple of cells, at greater
efficiency and far more stable voltage.

For switchers, amongst others, you could check out :-

http://www.zetex.com/
http://www.maxim-ic.com/
http://www.linear-tech.com/

If the prospect of entering into the (fascinating) field of switchers
is too daunting, go with regulators, but watch out for that drop-out
voltage. Bear in mind too that you should work to the worst case
condition, ie when the cells are nearly exhausted at 1.0 volt. That
means though that when the cells are full, you will be dropping a lot
of volts and wasting power. If you really don?t mind varying voltages
(and the units still work properly) then run the devices straight from
tapped batteries. Your sensor is a problem device though because you
cannot use any sort of resistor arrangement to give you a reliable 4.5
- 5.5 volts but five cells and a low-out reg will do it.

Good luck

Best

That sounds sensible. By having a slightly higher voltage battery pack
I could use a 5volt and 3volt regulators.

Do regulators use much power? Do they use power even if there is no
component drawing power? Can you give me some idea how much they would
use (for a 50mA regulator for example)?

The quiescent (or bias) current is a very good point. Sorry not to
have mentioned it. Some (generally older) devices take quite a whack,
up to 40mA for a 1 amp device though it tends to vary with output.
Best devices are down to less then a mA though.

Several other points :-

Negative line regulators are also readily available.

Some devices demand a specified load current before they regulate.

Some devices demand capacitors on input and / or output, some don?t.
But the caps should be of size and type recommended and placed close
to the device.

Adjustable regulators also readily available.

You?ll probably be fine with small plastic encapsulation devices
(TO92). As a design rule of thumb, though lots of exceptions, if a
component gets too hot to keep your finger on it then it?s too hot. A
simple calculation will determine suitability. I don?t recommend
surface mount components because you have to be very good with a
soldering iron to stick them down.

As far as I am aware, no simple regulators can sink current so you
have to make sure that your circuits returns current to ground and not
between regulator outputs. You probably won?t come up against this in
your circuit but bear it in mind.

Have a dive into your favourite component suppliers web pages and see
if they supply data sheets for potentially suitable devices. If not,
go the manufacturer?s site. Generally pdf format.

If you settle on your exact requirements and find what you think might
work but the data sheet doesn?t make too much sense (happens to me too
sometimes), post the device number and I can check it out for you.
(Might take a day or two to get round to it).

Best

My two cents:

A single rechargable lithium-polymer battery is going to give you an
excellent duration (much better than alkaline).  It's peak voltage is
4.2, 3.7 volts nominal, and it can go down as low as 3 volts.

The problem with a non-switching regulator is that, in essence, it's a
variable resistor.  It makes sure that its internal resistor value is
appropriate for the voltage, but other than that, it wastes just the
same as a resistor does.