What is the smallest thing you can see under a ...

Assuming that the other respond ants to this question are correct, I should add only one factor.  According to Wikipedia, the smallest objects that can be resolved under a light microscope is approximately 0.2 micrometers.  (This assumes that one only has access to such a light microscope, the ones that a single person can reasonably afford to purchase.  The others are so expensive that they can only be afforded by institutions.) 

See Wikipedia, Optical Microscope.

the wold strongest microscope is the "titan"

for more info http://www3.imperial.ac.uk/newsandeventspggrp/imperialcollege/newssummary/news_19-10-2006-8-26-26

as we are no more depended on light waves  to "see" things , there is a new vast scale to things we can see.

even particles smaller then the seen light wavelength.

search some of titan's  pictures, truly wonderful stuff.

I would like to add a little comment.

Using any microscope that is not light microscope doesn't enable you to see objects. Those apparatus only enable one to receive a computer simulation of the object. Why does it matter? because this means that the data you get is as good as the computer program used to calculate it. (Suppose there is some fundamental mistake regarding the understanding of elastodynamics all the data we get from this microscope is wrong).

indeed, the smallest thing you can see with your eyes is as long as the wavelength you can see, i.e. 350 nm.

Bacteria

The smallest things which are viewed beneath a microscope lens are viruses.  Electron microscopes are able to magnify them to visable sizes.  Scanning tunneling microscopes produce a view of what is detected at atomic levels.  They provide a good verification of what atoms look like.  One atom is only one angstrom in size.  Visable light is about 14 angstrom at its smallest.  Because of this an atom will never be able to be seen under a microscope.  Light waves/photons are too large to view such a small item.