Primary carbocation in addition of HBr to ethylene?
There is quite an evidence that carbocations are involved in this process, and that no concerted pathways exist for this transformation. 

While the case of ethyne may be difficult to analyse, lets consider 3-methylbut-1-ene:



If you consider the regular Markovnikov's rule to predict the product, you would probably get this:



While in actuality, the major product is actually this:



You can't really explain why that happens without accepting the existence of carbocations and the following mechanism:



This shows that carbocations are involved in the addition of $\ce{HBr}$ to an alkene.

Note: Since this question is about carbocations, I'd like to mention George A. Olah, a reputed chemist who studied carbocations by preparing them in superacid environments, where they were stabilized and studied using spectroscopid techniques. It was his research that led to the conclusion that carbocations have a planar structure. Have a look at his wikipedia page for more information.