Both the variant with of and the one without can be found, as seen in the following examples from the British National Corpus (BNC) and the Corpus of Contemporary American English (COCA):
(1) First of all, please, please, please, I beg you, don’t go on a diet. (COCA, Spoken)
(2) Sir Edmund, I beg you, wait a while. (BNC, Fiction)
(3) Lady Lavinia, I beg of you, don’t make me any gifts! (BNC, Fiction)
(4) Gentlemen, I beg of you, don’t let the Congress do this. (COCA, Fiction)
The examples are typical in that they show that the two phrases usually occur in archaic dialogue in fiction. Overall the two phrases are very rare outside fiction and they are both slightly more frequent in the BrE corpus than in the AmE one. The simple form without of is the more frequent alternative being 5 times more frequent than I beg of you in AmE fiction and 3.5 times more common in BrE fiction. In the Oxford English Dictionary the first attestation of I beg of you (from Othello, 1604: He begg’d of me to steale’’t.) is slightly older than I beg you (1675).
So, to conclude, you can use either I beg you or I beg of you, but both alternatives sound old-fashioned. Unless you want to sound like a historic novel when you speak, you can choose other alternatives such as the simple please.