Note: I am focusing on model of height-to-pressure relation in atmosphere, altimeter tries to follow and its limits of the model. There are, of course, limits of each particular instrument too, see answer by @ymb1.
[EDIT: I have added more details on various uses of altitude and some more details what could be the limit for measuring absolute altitude (it is not how thin air becomes, in fact), hope it answers your question better.]
Uses for altimeter reading
Height displayed by common mechanical altimeter should be pressure converted according to the International Standard Atmosphere (ISA) model. This model makes few simplifications (see the linked document for ex.), so it actually never gives exact height, except by chance. But as you are saying, it is anyway quite good approximation.
When you are flying, there is few different reasons why you would need to look on altimeter.
Obstacle avoidance, landing and maybe calculating final glide in glider. In this case it is really absolute height over terrain you need to know. To get this value you have to start with obtaining QNH, so already now altimeter itself is not enough (in any altitude) without external data. For greater precision you have to add more external data. You start with local temperature, but even then precision would be limited.
The magnitude of error does not depend on your absolute altitude though, but (in first approximation) on height difference between airplane and station/place your QNH comes from. So you are lucky if you want to land. Given QNH comes from that particular airfield, your altimeter should read exact value just on touchdown. If you need to avoid obstacles at similar altitude, error will be likely acceptable for practical use.
Again, it is not absolute altitude but relative difference what is causing this error. If you set QNH (or runway altitude) on airfield located 4000' above sea level and fly down to the see (let's say it is possible without traveling far away, so spatial change of air pressure is not an issue here), expected error of your altimeter will be similar as if you would fly 4000 feet up. It is because QNH (pressure at the sea level) is calculated based on the same model your altimeter is using, so model imperfections cancels out just at the altitude of this reference station.
ATC, mid air collisions etc. Absolute altitude is not important.
Instead, you need to be sure that two pilots who see distinct values on their respective altimeters can expect not being at same altitude. For this purpose simplest model with minimum of external parameters works best. As it is of foremost importance that all altimeters involved converts pressure to height in the same way. (Then, you need to expect pressure does not increase with altitude, but this is quite certain, as there will be always less air mass above you pressing down when you go upwards). Absolute altitude is completely unimportant here, or, for flying closer to terrain simple QNH-based offset will do. (Otherwise STD pressure setting is used.)
Even simple altimeter (in range of its physical limits of measurable pressure) would work quite well for this purpose in any practical height.
Aircraft performance and aerodynamics. That is service ceiling, choosing optimal cruise etc. These parameters are usually denoted in altitude in a POH, but only for convenience. It is air density what matters for anything aerodynamic related. And air density is air pressure corrected to temperature. So "altitude" provided by pressure-based altimeter is "just right" for this purpose, you can correct it based on local temperature and you have the best possible value. Again, this will work in any height (as long as POH and altimeter use same conversion between pressure and height).
Note that for later two uses value provided by altimeter is actually better than, say, GPS-based height.
Absolute altitude
OK, what if you really want to know your absolute altitude in stratosphere or even higher. Is it possible to use your altimeter then?
If the altimeter converts pressure to height based on ISA (true in most cases), the displayed value should be given by equation
$$
h=\left(153.85\,{\rm m\cdot K^{-1}}\right)\cdot T_0 \cdot \left(1-\left(p\over p_0\right)^{0.19026}\right)
$$
(see the reference above), where $T_0$ is specified to be 288.15 K (15 °C)
and $p_0$ is pressure you set in altimeter window. So, if you take such altimeter to space ($p=0$) it won't display more than 44 km (or 145,000 feet), given it won't reach it's physical/mechanical limits before. But, of course, the value becomes far from reality much earlier. Probably above the tropopause (10–12 km), where assumption of constant temperature decrease with height used in this ISA model becomes completely invalid. You could improve the model, but it probably won't work too well without more external data.
Nevertheless, problem is not that the air is thin. You can, in a way, measure air pressure even at low earth orbit few hundreds kilometer above ground. It is just the atmosphere what imposes (measurable) drag on satellites in low orbits. So yes, there is still something to measure and it is for sure measurable with right instrument. Problem is that you do not have any practical and "dependable" way how to calculate height based on this local pressure (only). Many other effects comes in play and you would need to know many other variable parameters in order to calculate altitude.
But, well, it was so already from beginning, wasn't it? You had to obtain right QNH (external info) even if you would fly in traffic pattern only. So the situation with altimeter at the orbit is not so much different actually.
While flying, you actually do not need to know your absolute altitude in many practical situations and pressure-based altimeter works perfectly regardless of height. If you need to know your exact altitude the limit is not air being to thin, but rather distance from closest station which can provide reference pressure.
With meteorological balloon located close to your aircraft and sending "QNH" for you (based on local pressure balloon measures and its known height, analogically to QNH coming from an airport), you could have quite good reading from (suitable) pressure-based altimeter even high in the stratosphere for example.
