Yes, you can target many countries, many individuals, races, gender, etc etc etc.
Now stop and think for a minute.
In order to reach a massive audience you would need - MASSIVE amounts of $$$
When you are doing PPC, you want to do targeting and segmentation of your chosen market.
The reason for this is that your adverts will be able to attract in an effective way a larger portion of your targeted market.
So for example. Say you have a dating offer, lets pick a black dating site.
If you simply decide to go out there and start spending money on your campaign, because you are believing that targeting more countries will result in more conversions, you will be wasting a lot of money.
1- Understand the offer that you are going to promote. You are promoting an offer which is for black people (black + black). Now, there might be other races which could be potentially interested in checking the site out, however, as you know, people in there are seeking for black people to date, so there is very little chance a white person would join the program.
2- Learn about your market. Continuing with the example; black dating site. Now that you know that you are going to put a focus on "black" people, you are going to need to segment that market. Think about the following: why would they join the program? how old are they likely to be? what kind of situations are these people in?
Once you have found an answer to that question you might know that you need to target 35-50 year old black males from the States.
3- LEARN EVERYTHING ABOUT YOUR SEGMENT. now, although this is critical in PPV, it will definitely help loads in PPC as well. You need to learn what does your segment like to do. Analise their trends, see where they like to go on the internet. An amazing source of information is "quantcast"; if a site is quantified, you will get access to super valuable information.
4- Set 2-4 test campaigns. Now with all of that information, you could probably argue that you know what your segment is likely to do. That being said, you still do no know about how effective will your offer be for the specific sites you will be advertising. Run 2-4 different campaigns based on your results and analyze which one has given you best results.
After that, rinse and repeat, escalate and do it until you start seeing a decrease in your conversion graphs (for a decent period of time, dont freak out in 1 day).
So if you were thinking about targeting many countries, the answer is NO unless you have a super big budget and you have so much knowledge in all of those segments.
Anyways, hope this helps you a bit.