Odin is the ROM Flashing Tool for SAMSUNG smartphones. ROM files flashable with Odin come with .tar extension.
Most of the ROMs you are going to flash with Odin are the official stock Samsung ROMs (or leaked stock ROMs). Custom ROMs are rerely flashable by Odin because they come with .zip extension that Odin does not recognize (it recognizes .tar files).
Custom kernels, however, are sometimes provided in .tar format by their developers (e.g. CF-Root kernels), so that they can be flashed by Odin. When your phone is new and running official firmware you most often cannot flash a custom ROM to it because a Samsung phone often requires a custom recovery and root rights that are included in a custom kernel to be able to flash custom ROMs. That's why Odin often comes in handy in rooting and flashing a custom firmware to your phone because you (often) can flash a custom kernel with it that already includes root and custom recovery and enables you to flash custom firmware (custom ROMs). I use the word "often" very frequently in the previous sentence because every Samsung smartphone is different and requires various procedures for rooting it and flashing custom ROMs (see the section about using Odin below).
If it comes to stock ROMs, the best source of stock (official) Samsung ROM files is located at this excellent website: SamMobile.com/firmwares (link). It requires registration (it's free) and I encourage you to set up an account there because you will most likely use this site several times during your stay at XDA. You will most likely come across 1 .tar or 3 .tar file ROMs there, flashable by Odin. Refer to the Odin flashing guide below for more info.
Below in this thread you can download Odin v3.09, v3.07, v3.06, v3.04, v1.85, v1.83 and all important versions of Odin Multi Downloader.
However, bear in mind that not every Samsung smartphone can be flashed using any Odin version. In fact, for every Samsung smartphone there's a specific Odin version compatible with it. Please refer to the tables below to learn which Odin version is compatible with your phone!
To use Odin with ANY Samsung phone you first need to properly install latest Samsung USB Drivers for Mobile Phones. You can download the drivers in this thread (link). They work for all Samsung smartphones. In that thread there is a full guide on installing the drivers on Win 8/7/Vista/XP x86 & x64.