I've designed a small, low part count (only 1 transistor), easy to build Geiger counter circuit which connects to the microphone jack and uses microphone bias voltage for power, converting its meager supply into 400v for the Geiger tube. Essentially, it is an adapter for connecting Geiger tubes as if they were microphones.
A video:

(Beware: the diagram you see in my video has a small mistake).

Here's the circuit diagram:

(printer-friendly version here, sch file here)

I also wrote a very simple open-source counting app for android, here's the github page and here's my latest build. It is very much a work in progress.

If you want to build this circuit for phone operation, before you start, it may be wise to make sure that the wired headset microphone port on your phone provides about 2.4 volts at up to a milliampere output (connect 2.2k resistor to it and measure voltage). Half or even just a quarter milliampere may be enough, any lower and you may need to raise value of R3.

You will need a TRRS connector to connect to the phone. The sleeve is actually the microphone input (positive), and the ring next to the sleeve is actually the ground. Note: the TRRS connectors I got at the electronics store were very bad and did not fit into the headphone jack unless filed down a little with a file. Do not force in ill-fitting connectors because that may damage your phone.

Transformer: primary: 10 turns + 10 turns 0.2mm (pins 1,5,2), secondary: 500 turns 0.1mm (pins 3,4), wound on 14mm diameter pot core. In retrospect, I probably should have used 5+5 windings - with 10+10 I was not getting +400v on the output without using a voltage doubler.
The core is not critical - you can just wind extra windings onto an inductor from a compact fluorescent light (using existing windings as the secondary), but then you might need a larger voltage multiplier as in the circuit below.
Wind the secondary first, then wind a few layers of saran wrap, and then the primary. I used an electric screwdriver at first but when winding secondary I switched to a DC motor from a broken printer, run at lower voltage.
When winding the secondary, make sure turns go all the way from one side to the other side, without leaving gaps so that upper turns do not fall near lower turns. But don't sweat it too much. Most of such wires can withstand over 1.8 kV. Also, it doesn't in any way matter that the turns lay neatly next to each other.
If you don't feel like winding the transformer, you can use an inductor from a compact fluorescent light leaving the original winding intact and adding an extra winding for the primary. You may need to add an extra stage to the voltage multiplier to get 400v with that.

I didn't count the turns in the secondary, I just filled the core's bobbin leaving a little space for the primary. For documentation purposes, I calculated turns from inductance relatively to the inductance of the primary. I had considerably fewer turns than I originally expected, mostly due to using a fairly loose-fitting bobbin that doesn't utilize all of the space in the core. If you want you can build a proper coil winder and use a magnetically activated switch to count the turns. You can then use MicroGeiger app to count the pulses from the switch with your phone :).

Board layout and pictures:

What looks like cold solder joints is a combination of lead-free solder and me being a programmer, heh. One thing to like about lead-free solder is that lead is usually contaminated with uranium decay products, and is consequently radioactive (doesn't matter so much for this circuit but matters for an ionisation chamber or a scintillator).
Soldering notes: either Zener diodes seem to be easily damaged by heat, or I got a bad batch of Zeners. It may be better to solder in a small socket for the Zeners, this will also make it easier to use this circuit for different Geiger tubes.



The case is made from PVC wiring conduit, with removable cover.

How this works:

T1,Q1,R3,R4,C3 form a blocking oscillator. It oscillates roughly as follows:
1: When the transistor begins to open and current begins to flow through T1.2-T1.5, the top part of the primary provides current through C3 and R4 into the base of Q1 for a time (it's supplying the bulk of the current by C3 being charged) - until the current into the base becomes insufficient to keep the transistor saturated.
2: When that happens, the collector current stops increasing, which causes the voltage at T1.2 to rise and the voltage at T1.1 to fall, which lowers the voltage at the base through C3, shutting off the transistor very rapidly.
3: C3 is now charged to >5 V, and the transistor stays closed until C3 discharges through R3, which takes much longer time. R3 determines the circuit's power output.
4: Once C3 discharges, a little current from R3 opens the transistor a little, then it rapidly switches itself on via the windings as described in step 1.

Note that with different values of components in a blocking oscillator, it can make several pulses as the transformer rings as an LC circuit (a pulse train), but ultimately the C3 will be charged and feedback will cease for a while.
C1,R2,C2 form a filter circuit that prevents pulses from the blocking oscillator from reaching the microphone and getting counted. With just one capacitor, if you plot the waveform reaching the phone you still see strong pulses from the blocking oscillator - that's why two capacitors and a resistor are necessary.
The transformer works as a step up transformer. Note that the primary voltage is considerably larger than supply voltage due to flyback effect.
D1,D2,C4,C5 form a voltage doubler. I originally intended to operate it without the doubler (with just a rectifier), but I got somewhat less than 400v. Next prototype, if I get around to making it, will not need a voltage doubler.
Z1,Z2 are Zener diodes which clamp the output voltage at 400v.
R5 is necessary for correct operation of the Geiger tube - to quench the discharge.
C6, R6 pass the pulses from the Geiger tube to the microphone. Their values are chosen to produce the RC time constant of about 1/30 000, which is close to the sampling frequency of 44100 Hz.
10pF is also the maximum parasitic capacitance according to the specs of the SI-22G Geiger tube. If you use long wires to connect your Geiger tube, put resistors close to the tube.
R1 permits the pulses from R6 to come into the microphone port. R6 and R1 also work as a 1/33000 divider, getting the ~100v pulses down to 3mv for the microphone. As a bonus, R1's low resistance permits the use of un-shielded cable (any interference signal in the cable has to drive this 100 Ohm resistor as a load). It looks a bit unbelievable that C6 can drive a 100 Ohm resistor, but C6 is not driving 100 Ohm resistor - it's driving the 3.3M resistor, with the appropriate time constant.
Some circuits connect the input to the cathode of the Geiger tube, which makes the Geiger tube a sizable antenna that picks up electromagnetic interference. My circuit uses the cathode of the Geiger tube as shielding.

A self contained circuit with a clicker:

This works much same as above, except that it uses a couple extra transistors to stop oscillation when there's no load, resulting in much greater efficiency at low counting rates - 0.01mA idle or so. This power saving does not matter for something powered off a smartphone because even without such regulation, the power consumption is only a tiny fraction of phone's power consumption, so I didn't include that in my phone-powered circuit).

It also includes a clicker circuit adapted from Charles Wenzel to drive a speaker or flash an LED.
You can use this together with a very low power microcontroller and run it off a CR2032 coin battery for years or indefinitely with a super-capacitor and a solar charger.
That could be useful for wireless rooftop radiation monitors and the like. Nuclear accidents are particularly likely to coincide with power black-outs.

Design tips for low power sensors

Use an overall design the power of which can scale down to zero (e.g. a blocking oscillator) where the pulses can be as far apart as you want by raising the resistor value.
Do not waste too much current into the base of transistors, put in just what's necessary given the hfe of the transistors
Know how much power you actually need (e.g. measure current consumption of a Geiger tube at specific counting rate) and design with that in mind.