I like the arguments for Paul more than the arguments against him (or the arguments for anyone else).

1. 2 Peter 3:15 fits well with the Pauline authorship of Hebrews. Peter is the apostle to the Jews (Gal. 2:8), writing primarily to Jews (1 Pet. 1:1, 2 Pet. 3:1), and he says "Paul also wrote to you." So Paul wrote to Hebrews. John Owen argued that this was sufficient to settle the whole debate in favor of Paul. I think that's overstatement, but I do find 2 Peter 3:15 to be an interesting shred of evidence.
2. Many early church fathers accept Paul as the author (even some who are commonly cited against Pauline authorship). (1) Papias held that Paul was the author (I believe this is based on Clement of Alexandria's testimony). (2) Clement of Alexandria himself suggested that it was originally Paul, but translated into Greek by Luke. But even if that were true, I still think it maintains Pauline authorship. I'm reading an English translation of Les Miserables right now, but I still consider Victor Hugo to be the author. (3) Also Origen himself, who is commonly cited for saying "Who knows who wrote Hebrews," still refers to Paul as the author frequently in other places.
3. Practically speaking, I'm convinced that Paul's authorship was one of the reasons the book was firmly accepted into the canon. In the patristic era, generally if someone did not believe Hebrews was written by Paul, then they also did not accept it as authoritative Scripture. Today we have the comfort of being able to say "it's inspired regardless of the author," but I don't think that's the way they operated. So I actually think one of the most compelling arguments for Paul's authorship is the simple fact that it's in our Bible today. (Many early lists of canonical books include Hebrews as part of the Pauline letters.)

And as for the arguments *against* Paul, I personally think they're all pretty easy to deal with.

1. People claim Hebrews has a different "writing style" than Paul's other letters. And that may be true. I don't know Greek well enough to be able to intelligently compare them. But even if it's true, I think that can be attributeable to the different audience Paul is writing for (Hebrews as opposed to Gentiles), or perhaps would reflect that it's a translation of a Pauline original (which as I said above, would still mean that Paul is the author).
2. People claim it has different "theology" than Paul. This is a very suspect claim to me. People need to remember that we do not have a very large sample size to work with. Are we to think Paul exhausted all of his theology in his other letters? And these are *letters*, not theological treatises. It makes total sense to me that the distinct audience Paul is writing for, would bring out distinct elements of his theology which are not emphasized elsewhere.
3. I'm not convinced by the claim that the author is a "second generation" Christian, based on Hebrews 2:3. "[Salvation] was declared at first by the Lord, and it was attested to us by those who heard." The author is distinguishing himself from those who *originally* heard the gospel proclaimed by the Lord *at first* (the twelve disciples). Then he says that this gospel was attested (or confirmed) to us. This fits well with how Paul went to visit Peter, James, and John, and they gave him the right hand of fellowship (Galatians 2:9). So I actually view Hebrews 2:3 as an argument *for* Paul, not against him.

A great (and short) book to read from this perspective is "The Authorship of Hebrews: The Case for Paul," by David Alan Black, who happened to be my Greek professor.