1. There are 23 countries currently have diplomatic ties with Taiwan ROC.
2. For many countries, they want the large PRC market. For example, in 1992, S. Korea after unsuccessfully pushed selling Taiwan navy frigates, in turn, they broke diplomatic ties with Taiwan and recognized PRC. Before, S. Korea was strong anti-communist country.
3. For US' case, when after then USSR and PRC relation went sour, US for purpose of reducing influences of USSR, built diplomatic relationship with PRC. But US also passed Taiwan Relations Act as US' own federal law. Taiwan Relations Act defines Taiwan as de facto country.
Even though Taiwan is not officially recognized by many countries, but passport holders of Taiwan ROC can visit 132 countries without needing to acquire for a visa. And Taiwan's charitable organizations and NGO have been contributing to the international community.