Looking for great violin CDs in solo.

Heinrich Ignaz Biber: Mystery Sonatas / Holloway, Moroney.

Bach: Sonaten & Partiten / Nathan Milstein

Brahms: Violin Sonatas / Itzhak Perlman, Vladimir Ashkenazy

Here's two solo, quite different from one another, the second being a bit more sophisticated in musical content and virtuosity. The first being rather stark and enjoyable renditions of Bach, which have been played better by others, yet nonetheless, this remains a favorite of mine and is very engaging in its presentation of these pieces (think violin coming from a deep, black space):

Lara St. John, Bach Works for Solo Violin

Vengerov Plays Bach, Shchedrin, Ysaye (worth it for the Ysaye)

Marco

Recordings of Violin and Piano (I'm unaware of any solo violin recordings) which I enjoy and would fit into your description would include -

Kyung Wha Chung "Con Amore" on London

Virtuso Vengerov on Teldec

Homage to Sarasate by Rachel Barton and Samuel Sanders on Dorian

Beethoven Violin Sonatas (Kreutzer & Spring) by Pearlman and Askenazy on London; and for something a little different

Rare Transcriptions for violin and piano transcribed by Saint Saens and Ysaye on Hyperion. The transcriptions of of a lot of music by Chopin and Saint Saens.

The Hyperion and Dorian CD's recordings are particularily outstanding from an audiophile POV, not that any of these are shabby. Some great playing and very assessible classical music here.

Second "Vengerov Plays Bach Shchedrin Ysaye" on EMI Classics
also
Naxos Prokofiev Violin Concertos Nos.1 and Sonata for Solo Violin. Tedi Papavrami, Violin and the Polish National Radio Symphony Orchestra Antoni Wit. Tedi Papavrami is a gifted violinist and the Sonata for Solo Violin in D major, Op.115 is incredible!

Arturo Delmoni: Songs MY Mother Taught Me

This Recording features Auturo on violin with Meg Bachman Vas supporting on piano. This CD is exactly what you are looking for. You'll love it.

Hilary Hahn, Bach Sonatas and Partitas on Sony. I give it about 3 plays a week. Also recommend Gidon Kremer's Beethoven Violin Sonatas on DG

Wow, fast respond with great quality I have received ever.
I'm looking them up right now. I just realize that it's not just violin but it could be viola, double bass... and the like... one like Yo Yo Ma plays.
My Sonus Faber sounds great with strings so I will probably get to Harps later on too.

YoYoMa = cello. Does that open up possibiities for you. Here is a quick recommendation of a cheap Naxos recording of very enjoyable/romantic music -

Virtuoso Cello Encores, Maria Kliegel & Raimund Havenith Naxos - One of my favorite compilation Cello recordings, but there are others, such as

Romantic Cello Favorites by Janos Starker & Shigeo Neriki on Delos.

There are a lot more.................

Yo Yo plays the cello. He should be very easy to get recommendations for. He's done some innovative collaborations over the years. The one that comes to mind is Appalachian Journey which I've only heard a few cuts from.

If you start to get into the concertos, for some remarkable performances check out the older mono recordings of Leonid Kogan on the Testament label. I especially like his Tchaikovsky Concerto.

Bach: The Sonatas And Partitas For Violin Solo / John Holloway

hilary hahn for bach violin..you can't go wrong picking up any hahn violin cd.

if you are going to open this up to more than just solo violin, your universe just exploded! Now you are talking the whole world of string quartets, piano trios, cello sonatas, etc. Here are some good choices featuring excellent performances of great music recorded well:

Schiff and Pereyi-Beethoven Cello sonatas on ECM
Floristan Trio-Beethoven Piano trios on Hyperion
Kashkashian and Levin - Brahms Viola sonatas on ECM
Takacs Quartet- Beethoven Quartets on Decca
Takacs Quartet- Schubert Death and the Maiden on Hyperion

An enthusiastic second to Jburidan's recommendation of the Biber Mystery Sonatas: absolutely magical stuff.

Second Gslone's Arturo Delmoni recommendation. Lovely, sweet stuff.

A few............

Viktoria Mullova plays Mozart Concertos Nos 1,3 & 4 -Philips.
Classic Perlman- Sony
Classic Kennedy- EMI
Hilary Hahn (any)
Pamela Frank plays mozart concertos 1-5 Arte Nova
Nigel Kennedy- Tchaikovsky & Sibelius Concertos- EMI
Nigel Kennedy-Mendelsohn & Bruck Concertos EMI.
Anne Sophie Mutter.

Another nod for Hilary Hahn. Check out Anne Sophie Mutter also.

You've been given some great suggestions here. For the "goosebump" factor, check out most recordings by violinist Itzhak Perlman.