Are there corporations in which I can invest with a clear conscience?

This is a good question, not just because corporations have been known to have environmentally destructive practices.

However, no two ethical questions, even just about pollution, are really the same. There might be some computer company gaining ground near you, and they might be looking for investors. You go and talk to them, and they say "our company does not pollute the environment", but then with a little digging you find out that they conduct all their business practices through companies that do. There isn't always a way to find out if what a company does goes against the type of world you want to live in, you have to do the research yourself. Now is probably the easiest time in the history of finance to find this type of information out.

And then there is another problem: isn't the overall prospect for success (i.e., returns on stocks and other financial instruments) also in a way an ethical concept as well as a selfish one? There are a lot of risky financial products out in the world of investing.

To be listed, a company must explain its operations in considerable detail in its prospectus. You may read these at your leisure and determine whether those operations and motivations are aligned with your beliefs and interests. I don't believe it's possible to answer this question any more specifically than that - your conscience is your own and doesn't align with anyone else's; it's up to you to determine whether a business' actions agree with your principles or not.

One problem to consider with this is that a company may meet 95% of your conscience requirements but may be missing something. Only you can decide what compromises you are willing to make, if any. There are many great investments all over the conscience spectrum.

The bigger problem I see with your question is that business is very global now. Even if you find a company that meets your requirements it is likely they do business and support one or more business that do not. How important is it to you and to what level do you take this conscience investing approach? If I like company A and they do everything I look for as a conscience investor but they source materials from company B that pollutes the environment and uses cheap foreign labor then is company A really all that great?

There are socially responsible ETFs, a Google search will return plenty of information. I would suggest something like that versus digging into each company individually.