When you have multiple replications of a study do you combine the data or analyze separately? Assuming that I have multiple replications of survey data, each one with exactly 1000 unique participants, do I run statistical analyses by combining the data into one large set of 3000 participants? or do I run the analyses separately? If one of these option is incorrect procedure, what is a consequence of doing it?
 A: Were all three samples randomly selected from the same population? 
If so then there is no reason you shouldn't combine the data together. I suspect that assumption probably won't hold though if you are dealing with survey data - are they from different time points? 
Combining the data gives you a large sample size with which to detect statistically significant differences. However, in doing so you want to ensure that there is not systematic bias in the data that you haven't accounted for - i.e. regional differences in your population or temporal effects, such as people attitudes shifting through time. 
Likewise, you don't really want to carry out three separate analyses if you can avoid it. Each one will have less statistical power (following the same logic as above), meaning you may not pick up on true differences (i.e. true positives). In addition, carrying out multiple tests can lead to type II error inflation, which essentially means you are more likely to generate false positives - these are ideally controlled for with familywise error rate adjustments.
So what do you do if you do have three datasets that are approximately the same but might contain systematic biases? Fit a mixed effects model, with a random effect for any potential biases. This effectively sweeps out any variation in your data due to the temporal/spatial effects that you aren't interested in and leaves you with greater statistical power to get at the questions you are interested in. 
There are some good packages in R to fit these models, as well as some comprehensive guides online for doing so if you are unfamiliar with them. 
