Is evolution true as Darwin said?
I saw an excellent public science talk a few weeks ago. The speaker presented 5 questions which, if you answer yes to, you can only come to the conclusion that evolution exists. Firstly though we should define evolution: Evolution is the change in the inherited characteristics of biological populations over successive generations. 

It was one of the best arguments I've seen put forward so I'll try to recreate it here. Put this to them and see what they say - and just in case they say no to any, I've put answers in for you ;) There is no hard evidence for the first four points because they are so damn obvious that if people say no, even after a logic based argument, then all they will ever say is no, they shouldn't need a scientific paper.

1) Do individuals reproduce? 

The answer to this is undeniably yes, you were the result of reproduction. Reproduction exists.

2) Is there variation among individuals?  

Yes, again this is undeniable. Do we all look and act the same? No. Are some people taller than others? Yes. Some more physically fit than others? Yes. Is everyone's hair or eye color the same? No. See, undeniable. Variation exists. 

3) Do some individuals die before they get to reproduce?  

Obviously yes. Children unfortunately die (of natural causes) which means they do no get to reproduce. Just go look in a cemetery or open the obituaries page of you newspaper and you'll likely find some one who died before they could have reproduced. Some people also never reproduce, because of life choices or fertility problems. Variance in reproductive success exists.

4) Do offspring resemble parents?  

The answer to this is also yes, when two humans reproduce they (normally) produce something that resembles a human. And when that human reaches maturity they will likely look a more like their parents than a random stranger. Personally I was looking at old family photos recently and I honestly though I had found a picture of me marrying my mother, that's how similar my dad and I look. Heritability of variance exists.

5) Does heritable variation lead to differences in reproductive success?

If you've answered yes to all of the above then you really should be answering yes to this one too. As a hypothetical illustrative scenario, imagine two male deer. One has big antlers and one has small antlers. The size of antlers is largely genetically determined. The male with big antlers is seen as more attractive by a female. She chooses to mate with him. She gives birth to his offspring (n=2, 1 male 1 female) who inherit his genes for large antlers. This repeats with several females in the population (n=10). The smaller male has fewer mating events (n=2) and therefore sires fewer males in the next generation. The next generation contains more males with large antlers (n=10) than small antlers (n=2). This is evolution, the change in the inherited characteristics of biological populations over successive generations.

Another example is humans. We know some men have low sperm counts leading to low probability of successful mating. Further, we know that male infertility can be genetically caused for example by Y-linked genetic defects. Therefore we can expect that males with low sperm counts, caused by Y-linked defects, will have fewer offspring than a healthy male (given equal opportunity to mate) and because all males inherit their fathers Y chromosome they too will have low sperm counts. They will be represented at a lower level in the population's next generation. Again, this is evolution.

Speciation:

It then doesn't take much to jump from this to speciation. It involves the introduction of isolating mechanisms. These can be things like geography (allopatric speciation), or sympatric mechanisms like morphology, behavior, or any trait which prevents one group of individuals mating with another. 

I'll illustrate first, and take the more difficult type - sympatric speciation. Again imagine our deer population. This time there is variance in sperm morphology, and female reproductive tracts. Males can produce two different types of sperm, one (male type S) is a slow moving but more resistant to the hostile female reproductive tract (because it is resistant to all types of antibody the females can produce), the other is faster (male type F) but less resistant (because it is resistant to only some of antibody the females can produce). Female reproductive tracts vary in the number of different antibodies they produce, one produces "all" that can be produced (female type R) and the other only a subset of the full array (female type W).

What will happen is that type S males will be more successful when mating with type R females because their sperm survive (whereas type F males have no sperm fertilizing the egg). However, type F males will be more successful in sperm competition than type S when mating to type W females. Repeated over many generations, these incompatibilities will cause distinct mating groups which do not overlap, i.e. species.

In reality it is much simpler to demonstrate this with allopatric speciation. Here two groups of one species become isolated by a geographical feature, like a river. Over time these populations evolve differently (because genetic mutation is random and selection might differ on opposite sides of the river). When they get the opportunity to mate after X generations, they can't because they have evolved genetic incompatibilities (offspring fail to survive, eggs can't bee fertilized).

One of the absolute classic examples is an experiment using fruit flies by Diane Dodd.   In her experiment she reared a population in two groups, one on starch based food, and one on maltose based food. After many generations (35 I think) the two groups showed mating preference, which is a reproductive isolating barrier, within their groups (mating pairs were more often formed from within treatments). Here is the paper.



Picture from http://evolution.berkeley.edu/