I downloaded the 64bit version of the Arduino software for Linux and I wasn't able to upload the code to the Arduino Uno board.
The error given by the IDE was:
java.io.IOException: Cannot run program "<install_path>/arduino-0021/hardware/tools/avrdude": java.io.IOException: error=2, No such file or directory
I checked and the avrdude file mentioned in the Java exception exists and has the right permissions (a+rx). However, it seems like it's compiled for a 32bit OS as vs. to 64bit:
arduino-0021$ file hardware/tools/avrdude
hardware/tools/avrdude: ELF 32-bit LSB executable, Intel 80386, version 1 (SYSV), dynamically linked (uses shared libs), for GNU/Linux 2.2.0, not stripped
The stock version on my OS (Debian testing) is compiled for 64bit and seems to work fine (I was able to upload firmware to the flash using the command line):
arduino-0021$ file /usr/bin/avrdude
/usr/bin/avrdude: ELF 64-bit LSB executable, x86-64, version 1 (SYSV), dynamically linked (uses shared libs), for GNU/Linux 2.6.18, stripped
--Tavi