I arrived in Morocco in October of 2014 and renewed my visa by traveling to Spain by ship for a day and getting my passport stamped again in January of 2015. My question is, am I allowed to leave the country and repeat this process this year by traveling again to another country, other than my own in order to return to Morocco for another 90 days? And if so, how many times a year is this allowed? I have read 180 days on some websites but there is not any clear answers anywhere about this that I can find.
Much like many countries (including the US), tourists can only stay for 90 days, as you've observed. That's what they consider a 'visit'.
Now like many countries world-wide, visits can be 'extended' by doing 'visa runs' or 'border runs' to come back in and get a fresh 90 days. Many travellers and digital nomads in South America and SE Asia do this on a regular basis.
Certainly, Wikivoyage mentions:
Tourists can stay for up to 90 days and visa extensions can be a frustrating and time-consuming process. (You may find it easier to duck into the Spanish-controlled Ceuta or Melilla and then re-enter Morocco for a new stamp).
Your own country's State Department website says:
For visits of more than 90 days, U.S. citizens are required to apply for an extension of stay (providing a reason for the extension) and should do so as far in advance as possible. If you are not granted an extension of your stay and you remain in Morocco beyond 90 days, you will be required to appear before a judge in order to clear your departure.
So all the 'official' advice is certainly to apply for a visa extension, but like other countries, hopping over the border seems possible too.
HOWEVER, and this is the key, you'll presumably be wanting to return on a tourist visa. Now the immigration officer (like in any other country - and I've had this line of questioning several times - especially in the US), they'll want to verify that you're not trying to just 'live' illegally in Morocco - ie on a repeating tourist visa.
So it'll be up to you at this point to show that simply, you've come to see and do more as a tourist, and the best way you can do that is to show your residence status in the US, proof of your address, and ideally, proof of a flight/boat out of Morocco as evidence that you have no intention of living there permanently.
In the US, for example, I had to show bus/plane tickets, and elsewhere I've heard of students being asked for evidence that they're actually studying back home, and others having their places of work rung up to confirm that they're actually still expected back at work.
Short version: There is no defined limit, but you'll probably have to prove you're a genuine tourist.
EDIT: You may also consider applying for a resident's permit - but that will obviously come with its own set of complications...
The best way is to go into the Spanish-controlled Ceuta or Melilla and then re-enter Morocco for a new stamp. I did that last time that I was in Morocco. If an officer at the border gets suspicious, just present him with about $10 US Dollars, and he will be more than happy.