From the evolution website talkorigins.org
"Q: Are there favorable mutations?
A: There are, but it can be hard to tell.
For a number of reasons it is not simple to give examples of favorable mutations. First of all, as we have seen, traits  may be favorable or unfavorable, depending upon the environment. Secondly it is not usually known to what extent a trait is genetically fixed and to what extent it reflects a reaction to the environment. Thirdly we don't usually know what genes effect which traits. Moreover a mutation may be favorable in the sense that it permits survival in an unfavorable environment and yet be unfavorable in a better environment.
However there are a number of good examples:
Antibiotic resistance in bacteria
In modern times antibiotics, drugs that target specific features of bacteria, have become very popular. Bacteria evolve very quickly so it is not surprising that they have evolved resistance to antibiotics. As a general thing this involves changing the features that antibiotics target.
Commonly, but not always, these mutations decrease the fitness of the bacteria, i.e., in environments where there are not antibiotics present, they don't reproduce as quickly as bacteria without the mutation. This is not always true; some of these mutations do not involve any loss of fitness. What is more, there are often secondary mutations that restore fitness.
Bacteria are easy to study. This is an advantage in evolutionary studies because we can see evolution happening in the laboratory. There is a standard experiment in which the experimenter begins with a single bacterium and lets it reproduce in a controlled environment. Since bacteria reproduce asexually all of its descendents are clones. Since reproduction is not perfect mutations happen. The experimenter can set the environment so that mutations for a particular attribute are selected. The experimenter knows both that the mutation was not present originally and, hence, when it occurred.
In the wild it is usually impossible to determine when a mutation occurred. Usually all we know (and often we do not even know that) is the current distribution of particular traits.
The situation with insects and pesticides is similar to that of bacteria and antibiotics. Pesticides are widely used to kill insects. In turn the insects quickly evolve in ways to become immune to the pesticides.
Bacteria that eat nylon
Well, no, they don't actually eat nylon; they eat short molecules (nylon oligomers) found in the waste waters of plants that produce nylon. They metabolize short nylon oligomers, breaking the nylon linkages with a couple of related enzymes. Since the bonds involved aren't found in natural products, the enzymes must have arisen since the time nylon was invented (around the 1940s). It would appear this happened by new mutations in that time period.
These enzymes which break down the nylon oligomers appear to have arisen by frameshift mutation from some other gene which codes for a functionally unrelated enzyme. This adaptation has been experimentally duplicated. In the experiments, non-nylon-metabolizing strains of Pseudomonas were grown in media with nylon oligomers available as the primary food source. Within a relatively small number of generations, they developed these enzyme activities. This would appear to be an example of documented occurrence of beneficial mutations in the lab.
Sickle cell resistance to malaria
The sickle cell allele causes the normally round blood cell to have a sickle shape. The effect of this allele depends on whether a person has one or two copies of the allele. It is generally fatal if a person has two copies. If they have one they have sickle shaped blood cells.
In general this is an undesirable mutation because the sickle cells are less efficient than normal cells. In areas where malaria is prevalent it turns out to be favorable because people with sickle shaped blood cells are less likely to get malaria from mosquitoes.
This is an example where a mutation decreases the normal efficiency of the body (its fitness in one sense) but none-the-less provides a relative advantage.
Lactose intolerance in adult mammals has a clear evolutionary explanation; the onset of lactose intolerance makes it easy to wean the young. Human beings, however, have taken up the habit of eating milk products. This is not universal; it is something that originated in cultures that kept cattle and goats. In these cultures lactose tolerance had a strong selective value. In the modern world there is a strong correlation between lactose tolerance and having ancestors who lived in cultures that exploited milk as a food.
It should be understood that it was a matter of chance that the lactose tolerance mutation appeared in a group where it was advantageous. It might have been established first by genetic drift within a group which then discovered that they could use milk. 
Resistance to atherosclerosis
Atherosclerosis is principally a disease of the modern age, one produced by modern diets and modern life-styles. There is a community in Italy near Milan (see Appendices II and III for biological details) whose residents don't get atherosclerosis because of a fortunate mutation in one of their forebearers. This mutation is particularly interesting because the person who had the original mutation has been identified.
Note that this is a mutation that is favorable in modern times because (a) people live longer and (b) people have diets and life-styles that are not like those of our ancestors. In prehistoric times this would not have been a favorable mutation. Even today we cannot be certain that this mutation is reproductively favorable, i.e., that people with this mutation will have more than the average number of descendents. It is clear, however, that the mutation is personally advantageous to the individuals having it.
Immunity to HIV
HIV infects a number of cell types including T-lymphocytes, macrophages, dendritic cells and neurons. AIDS occurs when lymphocytes, particularly CD4+ T cells are killed off, leaving the patient unable to fight off opportunistic infections. The HIV virus has to attach to molecules that are expressed on the surface of the T-cells. One of these molecules is called CD4 (or CD4 receptor); another is C-C chemokine receptor 5, known variously as CCR5, CCCKR5 and CKR5. Some people carry a mutant allele of the CCR5 gene that results in lack of expression of this protein on the surface of T-cells. Homozygous individuals are resistant to HIV infection and AIDS. The frequency of the mutant allele is quite high in some populations that have never been exposed to AIDS so it seems likely that there was prior selection for this allele. (See Appendix IV)
For a description of the recent literature consult the OMIM site for CCR5. "