Is a Masters Degree required to pursue a PhD? I recently heard someone saying that you don't need a Masters to pursue a PhD. Since I have never heard of people who got PhDs without Masters, I wanted to know whether this is true and how common is it for people to get a PhD without Masters?

I would also like to know if this is true for Engineering related fields specifically. 
In other words, can someone who has just finished their undergrad apply for a PhD?
A master's degree is not required for admission to a Ph.D. program, but Ph.D. admissions are extremely selective, and most students aren't competitive for a Ph.D. straight out of undergrad. In addition to a high GPA (I'd say around 3.8 or higher) and GRE SCORES (around top 10%, though this may depend on the program), you would need several publications/conference presentations, extensive research experience, and STELLAR letters of recommendation attesting to your readiness for a Ph.D. program. 

Most undergraduates, even with excellent GPAs and test scores, lack the research experience required for Ph.D. admissions. Also, undergrad (and to a lesser degree a master's program) is a time to explore your research interests. By the time you're applying to a PH.D. program, however, you're committing 4-9 years to researching a specific question/topic. Thus, you need to know exactly what you want to write your dissertation on and have to find a professor that will agree to take you on as a student. Again, most undergrads are still at the stage of exploring their interests, so they don't gain enough research experience in a specific topic. (I'm speaking generally in all programs.) 

This is why most people end up completing their master's first, but it's by no means a requirement, and if you do feel you're competitive for a PH.D. program and know what you want to research, then certainly apply to Ph.D programs. 

Disclaimer- I'm neither a professor nor a grad. student, nor is engineering my intended field. Again, my comments are meant more generally and apply to the U.S. 

Good luck!