The healing of Jairus' daughter in Mark 5:41 is described in the Greek New Testament in this way:

καὶ κρατήσας τῆς χειρὸς τοῦ παιδίου λέγει αὐτῇ· 
ταλιθα κουμ, ὅ ἐστιν μεθερμηνευόμενον· τὸ κοράσιον, σοὶ λέγω, ἔγειρε.

"And grasping the hand of the child, he said to her:
'Talitha koum,' which means, 'Little girl, I say to you, get up!'"

There has been some discussion in modern scholarship about whether or not the phrase "Talitha koum" constitutes a magic word in the context of Jesus' healing. Aside from that question, however, there are a few variants of this phrase in the manuscript tradition and it is not at all clear which form the author of Mark actually wrote. The first reading, and what many would identify as the earliest recoverable reading, is ταλιθα κουμ, which is attested, among others, in Codex Sinaiticus (01), as seen here:

There is another variant that is slightly different: ταλιθα κουμι. The variation between κουμ and κουμι reflects the difference in gender of the Aramaic imperative singular; Cranfield refers to this form as "Palestinian." κουμι is found in many manuscripts, including Codex Alexandrinus (02) as seen here:

The NA27/NA28 cite Alexandrinus as reading κουμι, but the exact reading, confirmed by the image above, is κουμει (itacism). 

Another interesting variant is found in Codex Washingtonianus (032) and a few other manuscripts: ταβιθα. Most exegetes attribute this variant to scribal confusion of the proper name Tabitha in Acts 9:40. Interestingly, it would seem that that story of Peter's healing of the girl in Acts 9:40 is modeled on this story in Mark. In Acts, Peter says to the girl, "Ταβιθά ἀνάστηθι." So in Acts, ταλιθα has become Ταβιθα, a proper name, and some scribe of Mark likely introduced this reading into Mark 5:41 on the basis of Acts 9:40—which is itself a mistake of Mark 5:41! Here is the reading in Codex W:

Now if that isn't confusing enough, then there is this bizarre reading of Codex Bezae (05): ῥαββι θαβιτα κουμι.

This is often explained as a mistake for ραβιθα, the Greek transliteration of the Aramaic dialectal form רביתא, meaning "girl." But if this is right, then how does one explain the doubling of the betas, and the (redundant?) ending βιτα? 

Another question concerns the origin of this saying. Did Mark's author create it? Did Jesus actually say it? If not, then why was an Aramaic expression used? Cranfield's concusion is that "the original words were remembered and valued as being the actual words used by Jesus on a memorable occasion" (The Gospel According to Mark, Cambridge, 1972, p. 190). What we do know is that some scribes wrestled with the reading, whether it was due to an unfamiliarity with the Aramaic language, a mistake, or a conflation with Acts 9:40.