What fraction of galaxies in the observable universe have we actually observed? There are a finite number of currently observable galaxies due to the finite age of the universe and the speed of light. What fraction of these galaxies have we actually observed (by eye, telescope, etc.)?
There are around 2 trillion galaxies in the currently observable universe according to the latest estimates, obtained by integrating theoretical galaxy stellar mass functions above $10^{6} M_{\odot}$ between $0 \leqslant z \leqslant 8$.

It's difficult to get a precise number for the total observed galaxies as the results from new surveys are being released all the time, and updated analysis of legacy data is revealing more galaxies. For example, the latest SDSS data release identified close to 200 million galaxies, whilst the ongoing Dark Energy Survey seeks to identify around 300 million galaxies. LSST, in Chile, will observe close to 20 billion galaxies, an order of magnitude greater than anything before it. However, all of these surveys operate up to relatively low redshifts. Probing to higher redshifts requires bigger, preferably space based telescopes, and much longer exposure times. As such, the high redshift universe has been poorly documented. Our understanding of galaxy formation at high redshift is not as complete as at low redshift, and so we may be under- or over-estimating the number of galaxies at this epoch.

A vague upper limit: we've observed less than 0.01% of all currently observable galaxies.