Does Bitcoin have inherent value if you can fork the project and create a new cryptocurrency easily? I like Bitcoin and I like the ideas to create a limited number of bitcoins. However, I see a lot of new crypto-currencies. It seems anyone could fork bitcoin, change something in the algorithm, and release a new crypto-currency. 

So I'm afraid that one could create hundreds of new crypto-currencies each day without any value. 

Is this a plausible scenario?
Yes, this is a real possibility. Effectively, Satoshi Nakamoto created a billion dollar market-capitalization of currency out of thin-air. Of course major corporations are going to attempt their own flavor, it is the nature of capitalism and it is a very healthy reality, which ultimately ends with a satisfied consumer. Progressive companies are forking it, prototyping new designs, and adding improvements. In the end, the quality, scale and technical effectiveness of your product will create the market-demand absent of billion dollar promotional marketing campaigns. BTC is a purely organic, community driven crypto-currency which sells it self. 

Currently, the infancy of BTC is very analogous to early 20th century automobile manufacturing. There were hundreds of car companies created in the US only of which 3 major manufacturers survived (Ford, GM, Chrysler). Analogous  to the rise of a myriad of crypto-currencies each of which claims to be better than the previous. How could you trust these crypto-currencies...? That is an unanswerable question which only the market will decide in the coming years. 

BTC is the first and most secure crypto-currency; its design and function are superior to many  other proprietary builds.