Student's t-Test
The Student's t-Test was formulated by W. Gossett in the early 1900's. His employer* had regulations concerning trade secrets that prevented him from publishing his discovery, but in light of the importance of the t distribution, Gossett was allowed to publish under the pseudonym "Student".
The t-Test is typically used to compare the means of two populations. Specifically, this java applet can be used to determine whether or not the means in two sample populations are significantly different. Nothing is assumed of the sample populations in this implementation. The sample variances are tested using the F statistic to determine whether or not they can be pooled (i.e., there is a reasonable chance that the samples came from the same population).
In order to keep everything as simple for the user as possible, the applet makes a few decisions regarding the samples automatically. The only real drawback to this occurs in the event that you've got some special information about the samples, which in my experience is often not the case. For example, if one of the populations comes from a very well characterized data set (known distribution), the applet's results will be conservatively erroneous, that is, tending to not see a significant difference when there might be one.
One precaution that should always be considered when using a t-Test: the sample data should be drawn from populations with normal distributions. Fortunately, this is often the case, especially with physical property measurements of materials. A good example of data that are typically not normally distributed are lifetimes.
*A brewery--the ultimate dream job of every mathematician!