What are your most favorite violin concerti?

"This is a "Sophie's Choice" question. It ought not to be answered."

Not at all. Sophie was forced to select someone to die; we're selecting things we love without destroying anything.

My personal favorites:

1. Saint-Saëns no. 3 in b minor
2. Tchaikovsky in D Major 
3. Bach Double in d minor4. Shostakovich no. 1 in a minor
5. Lalo Symphonie Espagnole
6. Bach concerto no. 1 in a minor
7. Barber violin concerto 
8. Sibelius in d minor

BEETHOVEN "VIOLIN CONCERTO" HEIFETZ - MUNCH
(Vinyl original RCA LSC)

or when digital is the way to go
same Concerto with Herbert v. Karajan & Anne Sophie Mutter
Deutsche Grammophone

Beethoven. Oistrakh/Cluytens on EMI
Mozart 5-I like Andrew Manze cycle the best.
Bach-Rachel Podger on Channel Classic 
Mendelsohn-take your pick here-I will go with Perlman or Michael Rabin.
Brahms-Leonid Kogan/Monteux and the Boston.SO
Bruch-Francescatti/Schippers NYP
Sibelius- Francescatti/Bernstein NYP
Barber-Vadim Guzman in BIS
Korngold-Ditto
Tchaikovsky-many favorites Heifetz/Reiner today’s pick
Shostakovich 1- Oistrakh/ Metropolous in excellent mono, Vengerov/Rostropovich in stereo.
Prokofiev 1&2- I like Steinbacher on Pentatone-not the flashiest but she seems to humanize them
works I have never grown to like-Bartok, Elgar, Britten

this survey ignores the bazillion Vivaldi,Tartini, and other baroque masters

All good choices, but I'm surprised nobody has yet mentioned the Stravinsky. His own recording with Stern (on CBS) is something of a disappointment, mostly due to Stern's intonation.
But there are some great recordings in the catalogue, like Chung with Previn (Decca, on vinyl coupled with the Walton), Perlman with Ozawa (DGG, on vinyl coupled with an equally outstanding performance of the Berg) and Mutter with Paul Sacher (on CD coupled with works by Lutoslawski, also on DGG).