For the Brandenburgs at least one Italian version seems a good idea - hmmm... Fasolis or Alessandrini? 
For concertos in general, I'm all with Bunny's recommendations of the "Concerts avec plusieurs intruments" series by Café Zimmermann (on Alpha). I hope they'll do some more, three issues is not enough. These include beautiful performances of the reconstructions for oboe (BWV 1053, 1055 and 1060), which is a major attraction for me.
I also bought the first volume with Mortensen on cpo, that Bunny pictured - really excellent, when complete it might even supersede Leonhardt in my mind. Similarity in approach too.
For the violin concertos I have only one favourite - haven't heard any recording that could match it to date!
The one and only, and still easily available - grab it!
Q
The Alessandrini Brandenburgs are excellent; they have no negatives. The set has 2 cds and 1 dvd of "extras" which I've played once and never played again. The Fassolis Brandenburgs are also excellent, they are every bit as good as the Alessandrini, and more fun! Their sound quality is SACD/hybrid, and if you have a 5 speaker SACD system then these are the only way to go. The SACD stereo layer is also warmer and more spacious than the stereo layer of the Alessandrini, so if you have a good quality system, then you will certainly prefer the warmer and more dynamic sound quality of the Fassolis. When evaluating the interpretations, again, reluctantly I have to give the Fasolis recording a slight edge. Everything that made the Giardino Armonico recording intriguing, the spontaneity, brisk rhythms, emphasis on horns, and irreverent attitude, is there in the Fassolis, but it's done so much better. In the Fasolis, there is so much pure joy in music making that it blows the competition away.
With respect to the Mortensen: The second set of the concertos is actually better than the first set! It sounds better and the play is slightly more fluent, as if the ensemble has finally reached a comfort zone where they can be in the music rather than merely performing it. It's a very slight difference, but if you hear the two cds together, you cannot miss it.
For the violin concerti, my favorite non hip version has always been the one with Isaac Stern and Itzhak Perlman on Sony. It's usually a budget choice, but those guys really had chops when they were fiddling and although it's unabashedly romantical play, it's very satisfying Bach. My other favorite non HIP recording is Akiko Suwanai's recording with the COE. The Suwanai recording wasn't released, unfortunately, in the USA but it is available from JPC.
For other HIP recordings, there is the 1990 recording by Hogwood with Jaap Schroeder, the Pinnock concertos with Simon Standage, and the newer, fresher interpretation, and better sounding release by the Akademie fur Alte Musik Berlin, which is the one I now prefer.
Please note: Simon Standage has recorded these concerti a number of times, with Trevor Pinnock and the English Concert; with the Collegium Musicum 90 (Chandos); with the Academy for Ancient Music (as director and soloist -- Harmonia Mundi). I have both the Pinnock and the Harmonia Mundi recordings, both of which are fine, if not in my top tier. Note: The Harmonia Mundi recording was also released in SACD, but I have the regular stereo recording so cannot comment as to it's sound quality.
Edit: The Harmonia Mundi recording is not with Simon Standage, but with Andrew Manze. I must have gotten a bit confused bouncing between threads. Which ever soloist, it still isn't in my top tier of favorites.
Edit: I pulled out the Violin concertos recording by Akademie fur alte Musik Berlin last night and was shocked to hear that it wasn't the recording I had been thinking of! Not that it isn't a very fine album, but it wasn't the one I was thinking of. For one thing, the AAMB's album had only one violin concerto, the triple concerto and the harpsichord transcription of the violin concerto. So, this morning I started pulling apart my collection trying to locate the album I had been thinking of, and after long (and enjoyable) searching and listening, I finally realized that the album I had been thinking of was actually Fabio Biondi's recording of Bach Violin Concertos, pictured below.
