So what was Jesus telling the man being crucified next to him? In the Concordant Literal New Testament, we read:
40 Yet answering, the other one, rebuking him, averred, "Yet you are not fearing God, seeing that you are in the same judgment!
41 And we, indeed, justly, for we are getting back the deserts of what we commit, yet this One commits nothing amiss."
42 And he said to Jesus, "Be reminded of me, Lord, whenever Thou mayest be coming in Thy kingdom."
43 And Jesus said to him, "Verily, to you am I saying today, with Me shall you be in paradise."
The original Greek manuscripts had no punctuation, and so commas must be provided by the translators. In the case of this verse, the placement of the comma is just as much a matter of interpretation as it is of grammar, so the fact that most English translations place the comma after "truth" (or "you") instead of "today (or "this day") simply shows the preferred interpretation of the translators, and not how the Greek has to be translated in order to be grammatically correct. The Greek adverb translated "today" or "this day" (sēmeron) may qualify either legô ("I am saying") or esomai ("shall you be"). And because either is grammatically possible, the question of where the comma should be placed when translating the verse into English must be determined by other considerations. Christ's words, "Truly, I say to you, this day you shall be with me in paradise," may just as legitimately be constructed as, "Truly, I say to you this day, you shall be with me in paradise." By placing the comma after "today" instead of "you," the fulfillment of Christ's promise need not be confined to the day in which they died, but may be understood as having its fulfillment at some time in the distant future. This translation is not only grammatically valid, but it makes Christ's words consistent with what the rest of Scripture teaches (as well as what Christ himself said) concerning the state of the dead.
In addition to the Concordant Version, J.B. Rotherham (in his Emphasized Bible) translates Luke 23:43 as follows: "Verily, I say unto thee this day: With me, shalt thou be in Paradise." It's interesting that Rotherham included a footnote giving the more traditional reading, even though he disagreed with it. Of course, he didn't have as much to lose as the people working on modern translation committees (who likely would not have been on the committees in the first place were it not for their commitment to "historic evangelical orthodoxy"). While holding a belief that the dead are actually dead (and thus functionally inactive and unconscious) would not be considered as serious an error as, say, a rejection of the doctrine of hell or of the trinity, this belief is still considered inconsistent with "historic evangelical orthodoxy," and would likely disqualify someone from being on the translation committee to begin with.
Objection: "Don't these translations make the word "today" redundant and unnecessary?"
Answer: Not at all. The word "today" (or "this day") was often used by the Hebrew people idiomatically, to introduce a solemn and important statement. According to this Hebrew/Aramaic idiom, "today/this day" often follows a verb of declaration, testification, command or oath, and emphasizes the solemnity and importance of the occasion or moment. Paul used this idiom in Acts 20:26: "Therefore I testify to you this day (semeron) that I am innocent of the blood of all of you" (Acts 20:26). This idiom occurs about 70 times in the Bible, with 42 instances being found in the Book of Deuteronomy alone (see, for example, Deut. 4:26, 39, 40; 5:1; 6:6; 7:11; 8:1, 11, 19; 9:3; 10:13; 11:2, 8, 13, 26, 27, 28, 32; 13:18; 15:5; 19: 9; 26:3, 16, 18; 27:1, 4, 10; 28:1, 13, 14, 15; 29:12; 30:2, 8, 11, 15, 16, 18, 19; 32:46; cf. Josh 23:14). Moreover, semeron appears in the LXX (the Greek Old Testament) and the NT 221 times.
In 170 of these places, the adverb follows the verb it modifies (some examples of this in the NT are Luke 2:11; 5:26; 22:34; Acts 20:26; 22:3; 24:21; 26:29; 2 Cor. 3:14, 15). There are thus 170 witnesses against 51 in favor of placing the comma after "this day." Therefore, it would not only be grammatically legitimate to punctuate Luke 23:43 with the comma after "this day" (so that the adverb follows the verb it modifies) it would also be consistent with how the word semeron is most frequently used in Scripture.
When we take the Hebrew idiom into account it becomes evident that, in response to the malefactor's request (which could very well have been a good-intentioned attempt at humoring a man that he believed to have been sincere and innocent but likely mistaken and/or delusional), Christ was in effect saying in response: "I give you my solemn word that you will be with me in paradise." Christ didn't say when they would be in paradise together - only that they would be.
Moreover, the earliest translation of the Greek New Testament was in the language of Israel's nearest neighbor, Syria. Syriac is a dialect of Aramaic, which most scholars believe Jesus spoke at least on occasion, if not regularly (for example, Jesus' words on the cross, "Eloi, Eloi, lama sabachthani" appear to be the Aramaic form of the words of Psalm 22:1). So it is a reasonable inference that in his reply to the thief on the cross Jesus spoke in the idiom that was common to both his own Aramaic language as well as the Hebrew language of the Hebrew Scriptures. It is therefore not surprising that in one of the oldest Syriac manuscripts of the Gospels (the 5th century Curetonian Syriac) the Hebrew/Aramaic idiom was evidently recognized by the translator. In this ancient manuscript the verse is translated so that the adverb "this day" clearly qualifies the verb "say" (and not "will be"): "Amen say I to you today that with me you will be in the garden of Eden."
By introducing the word "that" the translator removed the need for any punctuation to determine the sense of Jesus' words. And while it's true that the Syriac Sinaitic (the only other Syriac translation of the 4 Gospels that is thought to predate the standard Syriac version, the Peshitta) has the more common translation, the Curetonian Syriac (which, like the Syriac Sinaitic, predates all the English versions by hundreds of years) is still a very ancient witness for this interpretation of Luke 23:43.
Objection: "Nowhere else is Christ's frequently-used formula, "Truly I say to you" modified by an adverb of time. Thus, semeron should be understood as most likely being part of the expression that follows the "Truly I say to you" formula."
Answer: This objection loses its force when we take into account the well-known Hebrew/Aramaic idiom that uses "today/this day" to emphasize the significance and solemnity of an occasion. And who can deny the profound importance and solemnity of this occasion? This was one of the last things Jesus said before he died, and was possibly the last thing the man being crucified next to him heard anyone say to him before he died. It would therefore make sense for Jesus to speak in such a way on this highly exceptional and solemn occasion.
Objection: "In the instances where this idiom appears in the LXX we do not find the same verb word used in Jesus' "Truly I say to you" formula (legô)."
Answer: While this is true, this argument is undermined by the fact that the Hebrew idiom exhibits some variation in the verbs used; the only constant in the idiom is that the word "today" modifies a verb of declaration, testification, command, oath (etc.). In Luke 23:43 Jesus simply employed an idiom with which he and the thief would have been very familiar, and in a way that was most consistent with how Jesus normally declared things to people (i.e., using the word "legô").
The fact is, there is no reason to reject a certain translation based upon the premise that a particular construction must be found in other texts in order to be valid grammar. And it is not improbable that Jesus might have, on occasion, modified the introductory formula that he used most often during his earthly ministry. This is, in fact, the case in Luke 4:25. Here, Jesus modifies the expression and says "ep alhtheias de legô humin" ("I say to you in truth"). Here, "ep alhtheias" adverbially modifies "legô humin." As a result, it seems reasonable to conclude that the expression is not to be taken as an inviolable grammatical mantra.
Addendum: What is Paradise?
In the following audio message, Dan Sheridan argues that the "Paradise" which Christ promised the malefactor on the cross refers to life on the future earth:
 F. C. Burkitt, "The Curetonian Version of the Four Gospels," Vol. I, Cambridge, 1904.