The first data release from GAIA was in 2016 so fairly new. If you want to be certain you should take a look at it because as you say, GAIA will no doubt be the source of the most accurate parallax measurements in the near future. Speaking of accuracy, I believe that this is the essence of your question because it basically depends on how uncertain measurements you are willing to accept.
Basically, modern values of parallaxes are very small numbers, e.g. 0.1 milliarcsec which means a distance of
d(pc) = 1/(parallax in arc-seconds)
around 10,000 pc (one parsec is 3.26 light years). But the important point is the accuracy of these estimates. Clearly if your measurements is 0.1 milliarcsec, but the accuracy is 1 milliarcsec, it would be going out on a limb to postulate that you have measured a distance of 10,000 pc. So the real answer to your question is another question "to what accuracy?" So if you want something like 10 or 20 % accuracy you are more or less limited to our neighbourhood, say some 200 pc. If you check out ESA's website on stellar parallax, they will go up to 500 pc but it really depends on what level of accuracy your work requires.
If you check out the GAIA satellite then the aim is actually to go down to an accuracy of 24 micro-arc seconds so whatever object is measured to be farthest (with a given accuracy) is sure to replaced as the data from GAIA is analysed.
For fun, you might wanna look at this
also found at the GAIA website.. I think it provides a nice visual guideline to what distances we can expect (and it also nicely shows a ring at 500 pc - the limit of fairly accurate measurements from Hipparchos!)