Since Minecraft ships with Java 8 included, the version that I got was Java 1.8.0.25, you may run into compatibility issues with certain mods that don't play nice with that version of Java.

If you just updated Minecraft for instance, a separately installed Java version may still be used by the game. While that should work out of the box for most Minecraft players, you may run into issues. Once you have downloaded minecraft.exe on your computer and ran it, you will notice that it downloads the Java Runtime Environment and adds it as a folder to the root directory that you ran the file from. You can verify that this is the case right on the download page on the official website where it states under Windows that 'you don't need Java installed to run' the Windows versions of Minecraft. Mojang offers standalone versions of Minecraft for Windows that ship with an integrated version of Java that the game uses by default on new installations. Turns out that this is only partially correct anymore.