Short-lived species can go through hundreds or thousands of generations in that time period, which is ample time for substantial genetic change IF there is pre-existing genetic variation that can be selected for and against. If there isn't, evolutionary change would have to rely on mutation, and would be several orders of magnitude slower. Long-lived trees may go through no generations in 20-30 years, so cannot evolve, but even a single generation can lead to substantial genetic change if there is a high mortality, strong selection and variation for it to act on. Epigenetic variation can also be heritable, at least in plants, and may be an important source of adaptive capacity in long-lived species (or may not - the evidence is currently unclear!).

Every insect, weed, of fungus that has become resistant to a pesticide or overcome a resistant cultivar is an example. Bacteria that are resistant to antibiotics are another wealth of examples. Malaria resistant to antimalarial drugs.

Adaptation is often biochemical (i.e. target sites that are no longer sensitive), but can be behavioral (a mosquito that prefers to rest in a location that doesn't get sprayed). There is also the classic case of the peppered moth adapting coloration to match the polluted environment.

Of course, the number of specific examples will depend on what you mean by substantial adaptive evolution. Would new cultivars of wheat, apples, tomatoes, and other crops count? How about new breeds of domestic animals: rabbits, chickens, cows, cats, dogs, etc... Some of this does not have to be adaptive. Salmon that from a hatchery do well in the hatchery, but represent genetic pollution when released to augment wild populations.

Short-lived species can go through hundreds or thousands of generations in that time period, which is ample time for substantial genetic change IF there is pre-existing genetic variation that can be selected for and against. If there isn't, evolutionary change would have to rely on mutation, and would be several orders of magnitude slower. Long-lived trees may go through no generations in 20-30 years, so cannot evolve, but even a single generation can lead to substantial genetic change if there is a high mortality, strong selection and variation for it to act on. Epigenetic variation can also be heritable, at least in plants, and may be an important source of adaptive capacity in long-lived species (or may not - the evidence is currently unclear!).

Darwin finch beak size have been found to change rapidly over a short time in response to drought. See the attached for details.

https://www.sciencenews.org/article/gene-found-controls-beak-size-darwins-finches

I think that ecological change can be detected by the organism and as a result, one of apriori existing programs starts. That is, evolution is directed and fully pre-programmed. Mutations and selection play secondary role in evolution.  

Some possible examples that might fit:

Dispersal strategies of phytophagous insects at a local scale: adaptive potential of aphids in an agricultural environment By: Lombaert, Eric; Boll, Roger; Lapchin, Laurent

 BMC EVOLUTIONARY BIOLOGY   Volume: 6     Article Number: 75   Published: OCT 2 2006

Terrestrial insects along elevation gradients: species and community responses to altitude By: Hodkinson, ID

 BIOLOGICAL REVIEWS   Volume: 80   Issue: 3   Pages: 489-513   Published: AUG 2005

Local adaptation in pine needle scale (Chionaspis pinifoliae): Natal and novel host quality as tests for specialization within and among red and Scots pine By: Glynn, C; Herms, DA

 ENVIRONMENTAL ENTOMOLOGY   Volume: 33   Issue: 3   Pages: 748-755   Published: JUN 2004

LOCAL ADAPTATION IN THE ARMORED SCALE INSECT PSEUDAULACASPIS-PENTAGONA (HOMOPTERA, DIASPIDIDAE)

By: HANKS, LM; DENNO, RF

ECOLOGY   Volume: 75   Issue: 8   Pages: 2301-2310   Published: DEC 1994

This example does not show what you want. However, it may provide key terms or citations related to your question.

Deme formation in gall-making aphids Adelges japonicus (Homoptera: Adelgidae) By: Ozaki, K; Itahana, N

 RESEARCHES ON POPULATION ECOLOGY   Volume: 39   Issue: 1   Pages: 17-22   Published: JUN 1997

I am absolutly sure that you can have evolution (adaptations) with a secondary (or even none) role for random mutations and selection, as has been said, because organisms always keep something under their hats. They can suffer changes in their genic expresion patterns activating or supressing molecular pathways, due to ecological variations or catastrophes.

But we cannot stop wondering if there are random mutation and selection undergoing that fact. I think that if there is a substantial change through several generations and there is no change detected within the allele frequency, there is a chance that it could be alterations in the genic expression patterns.

Is this along the lines of what Guillermo was considering? Daphnia spine length is small if fish are not present. The spines increase in length in the population when fish are present.

Aquatic Ecology

March 1997, Volume 31, Issue 1, pp 89–98

 Tail spine length in the Daphnia galeata complex: costs and benefits of induction by fish

link.springer.com/article/10.1023/A:1009935100804

Details of the theory of partially-directed evolution can be found here:

Melkikh A.V. Quantum information and the problem of mechanisms of biological evolution. BioSystems. 2014. 115. 33-45.

https://www.researchgate.net/publication/258253080_Quantum_information_and_the_problem_of_mechanisms_of_biological_evolution

Article Quantum information and the problem of mechanisms of biologi...

A well documented expansion of an invasive ant, Linepithema humile, in southern California may be instructive. Andrew Suarez has authored several papers on the subject. In this Mediterranean climate species aridity and heat limited it to more mesic coastal habitats. Then, in more arid interior valleys they colonized landscaped suburbia. Now they are found well into undisturbed scrub habitats. All of this has transpired over a time scale similar to the one you seem to be interested in.

Best regards, Jim des Lauriers

Colorado potato beetle is an invasive species in Europe and Asia. It is a great example of adaptive evolution caused by  ecological change of environment, with applying of toxic compounds as well as its spreading far to the north and south of new area. See in: Alyokhin A., Chen Y.H., Udalov M., Benkovskaya G., Lindstrom L. Evolutionary Considerations in Potato Pest Management // Insect Pests of Potato. Global Perspectives on Biology and Management. - Ed. P. Giordanengo, C. Vincent, A. Alyokhin. Elsevier. - USA. – 2013. Part IV. - Chapter 19. - P. 543-574. ISBN 978-0-12-386895-4. 

To a large extent, it depends on what organism you're referring to.  As many of the answers already posted allude to, it depends on a number of things, including the strength of the selection pressure, generation time, mutation rate.  

For an example of how a substantial ecological change (historical metal mining) has caused evolutionary change over a short time in a vertebrate (trout), see the following paper:

Paris JR, King RA, Stevens JR (2015) Human mining activity across the ages determines the genetic structure of modern brown trout (Salmo trutta L.) populations. Evolutionary Applications. 8(6):573-585.

[Thanks Timothy – hopefully the link should now work]

http://onlinelibrary.wiley.com/doi/10.1111/eva.12266

My system did not like the link that Jamie provided. If I removed "abstract" from the link everything worked fine. What a wonderful example.

It depends if you are talking about adaptation in a strict sense. Or if you are lumping in acclimation as many people do when speaking more colloquially. Epigenetics provide an intermediate mechanisms for adjusting to change that straddles both adaptation and acclimation and can respond in relatively short time spans.,

If Mohamed still is not sutisfied by these explanations (If I were him, I wouldn't), I would recommend to look through the information on Baldwin effect, merely consulting Wikipedia, for example. The same mechanisms may work when any  characters or structures are evolving. There is a perfect work on this issue, of Kirpichnikov, 'Significance of adaptive modification for evolution". It is in Russian, but there is quite a long English summary in the end.  I would also recommend this work for our Russian interlocutors,  in order to avoid re-inventing the wheel

https://paw.princeton.edu/article/people-who-saw-evolution

“This was natural selection (from the killer drought) and evolution (from the passing of the genes for larger beak size) in action, witnessed over just two years.”

http://phys.org/news/2015-02-evolution-darwin-finches-beaks.html

"The Grants had shown that gene flow has occurred in the finches of Daphne Major during the past 40 years, but the new study found extensive evidence for gene flow throughout the roughly 1 million years that the birds have occupied the archipelago, which has helped the researchers update their understanding of how the lineages diverged over time.

"Read more at: http://phys.org/news/2015-02-evolution-darwin-finches-beaks.html#jCp