The newest, animated Svejk film was in production in the Kiev Yalta-Film Animation Department. The Yalta-Film web site is no longer on-line. The authorities in Russian-annexed Crimea said they have nationalized the Yalta film studiosThe former owners will be dealt with "in a civilized way"according to Russian president Vladimir Putin.
Похождения бравого солдата Швейка (2007)
(The Adventures of The Brave Soldier Svejk)
directed by Rinat Gazizov
screenplay by Robert Crombie
produced by producers Artur Novikov and Andrey Novikov
(whose bios used to be at the no longer functional domain of Yalta-Film)
The film appears to be in the portfolio of Rinat Gazizov's Ladybug Animation Studio.
Introduction clip was posted on Youtube by Robert Crombie.
This version of the animated film The Good Soldier Shweik is dubbed in Czech. It was presented by the Czech [public] Television's ČT art division. The film was distributed by NonStop Sales. (It is now defunct and their website has no content.)
Review by Lora Mjolnsness © 2015

Dobrý voják Švejk (1926, silent)
(The Good Soldier Svejk)
directed by Karel Lamač 
also with Karel Noll in the title role

Švejk v ruském zajetí (1926)
(Svejk in Russian captivity)
directed by Svatopluk Innemann 
with Karel Noll in the title role

Švejk v civilu (1927, silent [so mute the crazy Russian songs])
(Svejk in Civilian Life)
directed by Gustav Machatý, the director of Extasy
also with Karel Noll in the title role

Dobrý voják Svejk (1931)
(The Good Soldier Svejk)
directed by Martin Frič 
with Saša Rašilov in the title role 

Jiří Trnka's (and later his studio's) famous animated series (1955-2000)

Dobrý voják Švejk (1956)
(The Good Soldier Svejk)
directed by Karel Steklý

Poslusně hlásím, že jsem opět zde (1957)
(I dutifully report that I'm here again)
directed by Karel Steklý

Podoby Josefa Švejka (1983, 16min documentary)
(Faces of Josef Svejk
Bohumil Sobotka

????????? (1935)
We don't know the title of the American film that never was. But, what we know about it
starts with the following quote:
"Parts such as Kaspar Hauser or the title character in Jaroslav Hasek’s The Good Soldier Svejk were projects [Peter] Lorre always spoke about -- [Charlie] Chaplin even offered to direct Svejk - but failed to ever realize." - (from The Lost One: A Life of Peter Lorre By Stephen D. Youngkin • University Press of Kentucky. There are 17 pages with references to Svejk in Stephen Youngkin's book about Peter Lorre. The first nine are references to mentions of Svejk in the text of the book; the last eight are references to other sources mentioning Svejk. You might find the excerpts posted on quite interesting.

Soviet Union
Швейк готовится к бою (Shvejk gotovitsja k boyu) (1942)
[Svejk is getting ready for the fight]
directed by Sergei Yutkevich 

Новые похождения Швейка ("Солдатская сказка") [Novye pokhozhdeniya Shvejka ("Soldatskaya skazka") ] (1943)
(New Adventures of Svejk (A soldier's story) )
directed by Sergei Yutkevich

United Kingdom
Schweik's New Adventures (1943)
also known as It Started at Midnight 
directed by Karel Lamač
with Richard Attenborough [as railway worker]

The Good Soldier Schwejk (2019)
directed by Christine Edzard
(a film production of a theatrical stage performance with audience participation)

The Adventure of the Good Soldier Schweik, (1953)
directed by Geo Saizescu

West Germany
Die Abenteuer des braven Soldaten Schwejk, (1958) (TV)

Der Brave Soldat Schwejk (1960)
also known as The Good Soldier Schweik (1963, USA)
directed by Axel von Ambesser , starring Heinz Rühmann
Second Runner Up (Silver Globe) 1961

Schweyk im zweiten Weltkrieg (1961)
TV Movie 9 November 1961

Schwejking (2005, 30 min)
Czech, Polish (with English or German subtitles)
Nataša von Kopp

Schwejk's Flegeljahre (1963)
[Svejk's awkward age]
directed by Wolfgang Liebeneiner

Die Abenteuer des braven Soldaten Schwejk (1972 TV series)
directed by Wolfgang Liebeneiner

De Avonturen van de brave soldaat Schwejk (1968) (TV) 
directed by Anton Peters

Opowiesc o Szwejku i jego najjasniejszej epoce (1995) (TV)
(The Tale of Svejk and His Most Glorious Era)
directed by Włodzimierz Gawroński

Opowieść o Józefie Szwejku i jego drodze na front (1996) (TV)
(The Tale of Josef Svejk and His Way to the War Front)
directed by Włodzimierz Gawroński 

Przygody dobrego wojaka Szwejka (1999) (TV)
(Adventures of the Good Soldier Schweik)
directed by Włodzimierz Gawroński