I know most Jews in the Holocaust were simply shot and not put into death camps. But where are their bodies?
While some of these graves have been unearthed rather recently, most of these graves were destroyed during and towards the end of the war by Sonderaktion 1005.
In 1942 the former leader of Sonderkommando 4a, Paul Blobel, was charged with unearthing and burning the bodies buried during Aktion Reinhard (the killings in Sobibor, Treblinka and Belzec). This was in part due to a security or rather secrecy concern but mostly due to the fact that burying several thousand bodies in one place tends to lead to problems such as toxic sludge rising from the ground.
In May 1943 Himmler ordered the same thing done for the entire Eastern Front. Jews were used as forced labor to unearth the bodies, burn them and then crush the ashes and bones. Afterwards these Jewish laborers were shot.
The more the war progressed the busier Blobel and his people got. Mostly busy on the Eastern Front, detachments were also sent to the Balkans. Due to the nature of how it worked, the process itself was also bloody and murderous. Copied in camps such as Auschwitz, it also appears to have been rather effective though additionally to the graves themselves, what is often found today are the burial sites for the ashes ground from the dead bodies.
Sources:
Jens Hoffmann: „Das kann man nicht erzählen“. Aktion 1005. Wie die Nazis die Spuren ihrer Massenmorde in Osteuropa beseitigten.
Jens Hoffmann (Hrsg.): Diese außerordentliche deutsche Bestialität. Wie die Nazis die Spuren ihrer Massenmorde in Osteuropa beseitigten. Augenzeugenberichte und Gespräche, KVV Konkret, Hamburg 2013.
Yitzhak Arad: Operation Reinhard”: Extermintation Camps of Belzec, Sobibor and Treblinka
About 1,500,000 Jews were shot during the war, in smaller numbers in Poland and in massive numbers in the Soviet Union where most of the mass graves were located. As the war progressed and it became clearer that Germany might not win, the German authorities involved in the extermination of the Jews unleashed a giant effort to remove all traces of the genocide.
In the death camps in Poland - Auschwitz, Chelmno, Belzec, Sobibor, Treblinka and to a smaller extent Majdanek - the murdered, which totaled some 2,500,000, had initially been buried. Starting in 1942 and up until the early months of 1945 (in Chelmno for instance) camp authorities were ordered to have the corpses exhumed and burned. The actual dirty work was mostly forced on Jewish inmates.
The same thing happened with a large number of mass execution sites in the Soviet Union such as Babi Yar in Ukraine and Ponary in Lithuania, among many others. The whole operation was called Aktion 1005 and carried out by German SS and police forces overseeing Jewish prisoners.
To give a broad answer, all over Eastern Europe and the Russian plains. The Nazis (and Russians, to a certain extent) rounded up Jews and executed them all over. You can probably understand why precise, detailed records weren't kept for the majority of these mass graves.
To answer your question; there are plenty of identified mass graves that still survive, a lot are unknown, and more than a few have already been exhumed and the remains re-interred more respectfully elsewhere. A few of the big examples of surviving mass graves include the following places:
Katyn Massacre: The Red Army/NKVD killed 20,000+ Polish POW's and Jews in 1940, the mass graves were partially disinterred in 1943. This is a definite, verified, known site of a giant mass killing field.
The Wola Massacres resulted in the deaths of ~40,000-~50,000 Poles during the early stages of the Warsaw Uprising. Various satellite execution sites have been positively identified, along with the resting places of bodies and ashes.
Thousands of other small, un-identified sites played host to the executions of small groups of Jews, Poles, and other undesirables.
Other famous mass-grave sites (Babi Yar, Rumbula, etc.) were partially/wholly disinterred and eradicated by Sonderkommando units and other labor later on in the war. While there may only be small amounts of bodies left or the massacre sites completely eradicated, there are simply too many survivors who's accounts all match up to call these events fiction.
Edit- Stuck-through a factually incorrect statement.
Check out the book The Holocaust by Bullets. It's about a priest's search for these mass graves. About 1.5 million Jews were killed and buried in mass graves outside of their villages, without being transported to concentration camps. These mass graves are still there and people in the towns know where they are. The priest and his team uncovered many of these. It is a time-consuming process and the generation who knows where they are are dying off.