What are your most favorite violin concerti?

Mine are:

Tchaikovsky Concerto in D,
and Mendelssohn's in Em

Many would argue with me but I think the best of them all by far is from Beethoven. I know a lot of people including those in the academic circle believe it's the Tchaikovsky concerto.

But anyway that's only my opinion.
Tchaik's. Tied for 2nd are the Beethoven*, Brahms, and Sibelius, with the Mendelsohn close. I love the Barber until the 3rd movement, so it's gorgeous-but-short for me.

* Did you know that Ludwig himself wrote a 6th piano concerto by adapting the VC to the piano? It was startling for me the first time heard, but I really like it. My favorite performance (of the few) is Spada's with Gibson and the Philharmonia on ASV.
Brahms, but I admit the Beethoven may be as fine a piece of music (the Bach double, also). Good though they are, the others are not in the same league. I like the Bartok, Prokofiev (2nd), Sibelius and Berg (love the Berg) at least as well as -- more than, really -- the Tchaikovsky and Mendelsohn. Many great performances of each, of course, but Szeryng never misses.

JSB d minor for two violins
WAM number 4

not necessarily in that order
In addition to Beethoven, Brahms, Sibelius, Mendelsohn and occasionally Tchaikovski, I can enjoy Bruch, Dvorak(!), Barber, Prokofiev, and Mozart. Dvorak gets more play time as I'm rather fond of Czech music.
For me, in order:

1) Tchaikovsky (unassailable, in my opionion)
2) Dvorak (close 2nd to Tchaikovsky, if that's possible)
3) Mendelsohn
4) Sibelius
5) Prokofiev
6) Glazunov

Michael, I'll second your list and your ordering, with the exception that at #6 I'd do this:

6) Wieniawski's 2d
7) Hendl
8) Glazunov

Great list. But, then I'm still missing from my list concertos I really enjoy by Arensky, Barber, Bartok, Berkeley, Bruch, Martinu, Menotti, Segerstam...
My favorites in the following order are:
1. Beethoven
2. Brahms
3. Sibelius
4. Dvorak
5. Lalo (Symphony Espagnole)
The above in that order, then the following in any order: Tchaikovsky, Wieniawski, Bruch, Vieuxtemps, Mozart No. 4 & No. 5, Paganini

There is also much joy in listening to the various versions and critiqueing them. i.e. I thought the early version of Anne-Sophie Mutter playing the Beethoven with Herbert von Karajan was lacking in many things, but her new version with Kurt Masur and the New York Philharmonic is extremely good and can vie for the best among contemporary versions.

I think Heifetz still reigns supreme among many of the available recordings, and particularly with the Sibelius. He had no recording of the Paganini because as he said that was "for the rest of them".
This is a "Sophie's Choice" question. It ought not to be answered.
"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.