Can I have two campaigns in the same niche, but two different domains running through adwords? For example lets say I have two affiliate sites and I want to do the another one in the same market with the same keywords just in another campaign?
You can't do it with the same keywords because google doesn't allow showing multiple ads from one account for one keyword.
Yes, you can. Although Google will only show 1 domain at any one time. I'm assuming for example you have campaign A and campaign B. Campaign A is promoting the keyword [tea bag] and showing Domain 1 Campaign B is promoting the same keyword [tea bag] and showing domain 2. When someone searches for [tea bag] Google will randomly trigger one of the ads from either Campaign A or Campaign B and consequently display Domain 1 or Domain 2. It won't trigger them both. It's against Google's policy however, to have 2 accounts, in order to be shown twice for the same keyword. That's my answer if I've understood you correctly.
you can do what you want to do, but only 1 domain will be shown at a time. You cannot take up 2 ad spots per keyword with one account
If you're going to try to break their rules, be prepared to have your accounts banned. It's just a bad idea and your competitors are the ones who will report you.