Short Answer: There are all sorts of opinions on this topic, but I will present what I believe to be the most clear and coherent argument - from Scripture, logic, history, and observation - which is that the gifts have always been "offered", but not always "accepted". Thus, it can be seen that both the cessationist and non-cessationist views are built upon some truth: the former, historical; the latter, doctrinal.
I grew up in conservative churches (Nazarene, etc.), got "saved" and "baptized in the Spirit" in a Latter-Rain Movement church, spent some time in an Assemblies of God church, and am currently serving in ministry at a Baptist church. I have heard, accepted, and believed each of the major positions at various points, and now feel that I understand the topic well enough to make a claim about the truth.
Scriptural Groundwork
First, "receiving the Holy Spirit" is the same as "the baptism in the Holy Spirit." (See here for full justification.) As such, there are not two classes of Christians (the "saved" and the "charismatic"); if you are born again, you have been baptized in the Spirit.
Second, this baptism is a promise to all believers for all time:
And Peter said to them, “Repent and be baptized every one of you in the name of Jesus Christ for the forgiveness of your sins, and you will receive the gift of the Holy Spirit. For the promise is for you and for your children and for all who are far off, everyone whom the Lord our God calls to himself.” -Acts 2:38-39
This passage is in the context of an explanation of the "baptism" of Acts 2, not the isolated (and often misinterpreted) statement of John 20:22.
Third, the gifts are given according to the will of the Spirit, and are exercised according to the obedience of the individual. That is to say, if you don't speak in tongues (for instance), either the Spirit hasn't given you that gift, or you aren't walking in it.
Fourth, the gifts did "cease" (as far as we can tell) after the time of the Apostles. There may be exceptions, but let's face it, the scene in Acts was not the scene in AD 500.
However, it would not be correct to say that "because the gifts ceased, it must have been because God wanted them to cease." That's just bad logic.
It would also not be correct to say that "because the gifts ceased, they are not for today." It is entirely possible that the gifts are not in widespread operation today because modern Christians are unwilling to step out and look like a fool (by claiming to have a message from God, for example.)
A More Subjective Argument
To argue that "the Spiritual gifts are not for us today", one would have to show that the Spirit does not want believers to move in these gifts today. Since the gifts were given to empower the church for ministry, build the church, and edify the church, I think it is strange to argue that they were only needed during the time of the Apostles; the job is not yet complete! We still need His help! The argument becomes stranger when we consider that there is not a single passage of Scripture to support this! If we were to just look at Scripture, and ignore history for a moment, it would seem clear the gifts were intended for every generation.
The confusion comes in when we look at history and ask "why do they appear to have ceased?"
Some claim that God didn't want them in operation anymore, but this argument is unfounded.
The alternative is: the church began to reject the gifts of the Spirit - or at least, those gifts which were most uncomfortable! (People generally don't claim that "teaching" or "evangelism" or "exhortation" has ceased... but when it comes to "healings" or "tongues" or "prophecy" they get nervous.)
With all of that "reasoning" aside, I can testify personally to the fact that all of the gifts are in operation today, but are not in widespread operation. There are some who give themselves over to the Spirit when He leads them to lay hands on a person for healing; some who will prophesy; some who will give with liberality. But let's face it - this stuff is 100% rejected by modern post-Enlightenment (humanist) thinking. It's not "science" so it can't be true. But it is true.
However, I can also testify that there are many "charismatic" things going on that are driven more by emotion and mimicry than the Spirit. If a "prophecy" about the future doesn't come true, it wasn't coming from a "Spiritual gift" in the first place. If a person can "pray in tongues" before they are even in relationship with God, it wasn't coming from a "Spiritual gift". (Not to mention some of the made-up gifts modern churches have invented.)
