The rate of mutation has been studied since the early 1900s, which is when your question was put to rest in a prescient paper by JBS Haldane (1949). Essentially the answer is that it varies a lot between organisms and environmental conditions, but for any given gene a mutation occurs once in about 50,000 sexual replications. That is equivalent to, in a human, several hundred new mutations in each person born. Impressively, Haldane's calculations have since been confirmed by a variety of other methods (e.g. Nachman & Crowell, 2000; Xue et al., 2009).
Faster rates of evolution have been recorded in other organisms, and there have been many, many studies looking at the rate of increase in sizes of the whole body or of particular organs of a wide variety of animals and plants.
For example, Azevedo et al. (2002) look at the rate of mutations affecting size (trying to select for decrease in body size) in C. elegans, and found mutations affecting size occured at a rate of ~0.0025 per haploid genome per generation.
In another example, with a result more definite regarding your question, Keightley (1998) investigated the rate of change in average body weight under conditions of selection for increased body size, over 50 generations in mice. They recorded an average increase of 0.23-0.57% body weight per generation from new mutations. That's pretty huge, and demonstrates how rapidly a complex trait can change by mutation under selection.
I wrote a small piece of python code to calculate the increase after x generations at the same rate (the formula is very simple)...
initial = 1
rate = 0.35
generations = 1000
result = initial * (1.0 + rate) ** generations
Thus if we assume that approximately the average rate found in the mouse study (0.35%) could be the rate at which giraffes' necks might increase under strong selection, after 1000 generations the mean neck length would be over 20 times the original length. A low estimate for wild giraffe longevity is around 20 years, thus for giraffe necks to increase around 20x might take 20,000 years. Of course this basic estimate is making a whole lot of assumptions, but the point is that rates of mutation are actually very high, easily enough to explain the diversity of traits we see in the world.
- Azevedo RBR, Keightley PD, Laurén-Määttä C, Vassilieva LL, Lynch M, Leroi AM. 2002. Spontaneous Mutational Variation for Body Size in Caenorhabditis Elegans. Genetics 162: 755–765.
- Haldane JBS. 1949. THE RATE OF MUTATION OF HUMAN GENES. Hereditas 35: 267–273.
- Keightley PD. 1998. Genetic Basis of Response to 50 Generations of Selection on Body Weight in Inbred Mice. Genetics 148: 1931–1939.
- Nachman MW, Crowell SL. 2000. Estimate of the Mutation Rate Per Nucleotide in Humans. Genetics 156: 297–304.
- Xue Y, Wang Q, Long Q, Ng BL, Swerdlow H, Burton J, Skuce C, Taylor R, Abdellah Z, Zhao Y, et al.. 2009. Human Y Chromosome Base-Substitution Mutation Rate Measured by Direct Sequencing in a Deep-Rooting Pedigree. Current Biology 19: 1453–1457.