There is not and there can not be any general rule. It really depends on the subject matter you are studying. Therefore I would prefer unstandardized coefficients for interpretation to see the units that are of interest.

What happens if the DV goes up by .25? If you are talking about administering a drug and that increase kills the patient it is important. Best wishes.

I think that in social sciences, where the variability of survey variables (opinions) is usually high,  r = 0.25 (if it is statistically significant) means something and you can predict Y with standard error and confidence intervals. But when you must have more precise prediction, sometimes even r =0,90 isn't enough (if we are talking about measurements by calibration functions of instrumental chemistry or physics). I have read  some papers on sociometric and even on econometric themes when the autors had confirmed significant effect by r less then 0.25.

I think it depends on use and on statistician...

There is not and there can not be any general rule. It really depends on the subject matter you are studying. Therefore I would prefer unstandardized coefficients for interpretation to see the units that are of interest.

Statistical significance is the least interesting thing about the results. You should describe the results in terms of measures of magnitude –not just, does a treatment affect people, but how much does it affect them. With a sufficiently large sample, a statistical test will almost always demonstrate a significant difference, even there is only very very small differences exists. When the difference is very small, even it is significant, it is often meaningless. Thus, reporting only the significant P value for an analysis is not adequate for readers to fully understand the results. Statistical significance is the probability that the observed difference between two groups is due to chance. If the P value is larger than the alpha level chosen (eg, .05), any observed difference is assumed to be explained by sampling variability.

Hence when we discuss the effect or difference, effect size is often used. It is the magnitude of the difference between groups. The absolute effect size is the difference between the average, or mean, outcomes in two different intervention groups. The effect size refers to the raw difference between group means, or absolute effect size, as well as standardized measures of effect, which are calculated to transform the effect to an easily understood scale. For two independent groups, effect size can be measured by the standardized difference between two means, or mean (group 1) – mean (group 2) / standard deviation.

The effect size is the main finding of a quantitative study. While a P value can inform the reader whether an effect exists, the P value will not reveal the size of the effect. In reporting and interpreting studies, both the substantive significance (effect size) and statistical significance (P value) are essential results to be reported.

for details about effect size see:

https://en.wikipedia.org/wiki/Effect_size

Good points, Yuanzhang. But here you went wrong:

"While a P value can inform the reader whether an effect exists,..."

Not even this is the case. P values don't do that. They only tell us how likely we should expect "more extreme results" than the one observed for a given functional and statistical model with a particular restricted hypothesis about a parameter in the model (i.e. the null hypothesis). Espesially for larger samples the p-values are influenced by both, the possible presence of an effect and the possible mis-specification of the model.

And, interestingly, the question for the "existence" of an effect is philosophically nonsense, because i) some non-zero effect will always exist [due to the fact of the non-infinity and the granularity of our universe], and ii) models are not the truth itself; they are simplifications, and therefore always "wrong" to some extend and with respect to some features.

I am not sure why p-values should be reported at all. Well, they are expected by the majority of the audience, and therefore they should be reported - but this is a "career argument" and not a scientific argument. The effect estimates are uncertain to some degree, and this uncertainty has to be reported. There are several options, and the p-value is one of these options, although, to my opinion, the worst (because it is the least informative, least relevant, and most often misunderstood statistic). Better choises were confidence intervals, likelihood intervals, or credible intervals. These intervals are just intersections of more complex structures that represent our "knowledge" about the estimated values (i.e. the sampling distribution, the likelihood function, or the posterior distribution). Not all their characteristics can be summarized in a single simple interval. The best would be to provide the underlying structure, but that is difficult to communicate and to use. If particular features of these structures are of interest (like a profound asymmetry, one can even think about a possible bi- or multimodality! etc.) one can describe this with additional statistics, e.g. by giving a intervals at several sections (like a 10%-LI and a 5%-LI, or a 50%-CI and a 90%-CI, or a 90%-CI and a p-value, something like this).

I agree with David Eugene Booth. And i will wonder what variables explains the remaining variance, and how many variables are in the model.  

"Cohen (1988) hesitantly defined effect sizes as "small, d = .2," "medium, d = .5," and "large, d = .8"  --->  http://www.uccs.edu/lbecker/effect-size.html 

I too think that there is no general rule and that you have to make a choice and persuade others of the practical adequacy of the size of effect you have found in the context that you are working in.

I have used this example before on Rgate but it bears repeating............... In a trial of the effect of taking aspirin on heart attack the odds ratio was so dramatic that the trial was stopped and placebo group advised to take aspirin. The odds ratio of a heart attack for placebo compared to taking aspirin was a lowly 1.83, while the R2 was a puny 0.0011; yet this was sufficient for action.

The community of researchers were convinced to take action with an effect generally considered small.

Thanks for the response. But need read whole sentence:

While a P value can inform the reader whether an effect exists, the P value will not reveal the size of the effect.

Or you can read as "When (if)  a P value can inform the reader whether an effect exists, the P value will not reveal the size"

In general, there is no rule  to judge or answer the question  "And i will wonder what variables explains the remaining variance, and how many variables are in the model.  "

But you really want to make the selection by statistic, you can use AIC (Akaike information criterion) or BIC (Bayesian information criterion) for the model with different variables. The smaller of AIC (BIC), the better.

I see you point, Yuanzhang,

but a P value has no such property that it "could inform the reader whether an effect exists".

The P value informs the reader about what his/her expectation to observe more extreme effects should be, w.r.t. to a hypothesis within a given model, and given the data. Often the hypothesis is chosen to give a model with an effect size restricted to zero, so a small P value indicates that more extreme data should be unexpected in a model with the respective effect set to zero.

Note that all this has nothing do do with the existence of any effect size, and also not with the estimation of the effect size. The only thing that is able to "inform the reader whether some interesting effect exists" is the combination of the estimate of the effect (in conjunction with some measure of its uncertainty) and the agreement on the (reasonability of the) model. For instance I could analyze my waiting times at the supermarket cash desk and compare it with the waiting times of customes at other cash desks. I note that my average waiting time somewhat higher than that of other customers. Would a P value of 0.01 inform me that there is a natural law determining that I do have to wait longer than others? I think not. Would a P value of 0.99 inform me that that there is no difference in waiting times between me and others? (I also think: no).

Why don't the observation(s) of lottery winners inform us that there exist psychic powers? After all, the P value to win the lottery by guessing is very, very, very low.