Files in the SD or USB are owned by ROOT and have the default permission set to 666 which everybody can read or write but not execute.

To change this behaviour,

1. start the console (Ctrl+Alt+T)
2. type sudo nano /sbin/probedevice
3. on line 43,44 change noexec to exec, fmask from 111 to 0 (line says *FAT* and *msdos* at the beginning)
4. save and reboot

http://forum.eeeuser.com/viewtopic.php?id=954 credit goes to Damaniel

by zedkatuf

1. You might have to reformat the card as ext2 to allow applications to run properly. The forum link above shows that many users have had issues with trying a fat-formatted card to run excecutable files. If your USB or SD card is big enough, you could reformat it with two partitions (back-up first!!), one which is vfat, the other ext2. Then, put all your applications on the ext2 partition & mp3's other files on the vfat partition.
2. Instructions below for how to do this, if you want to divide up your sd card in this manner. The instructions end up with you splitting the sd card in two, the first partition is windows-based, the second linux. Making the first parition windows-based (FAT16 or FAT32) helps for when you put the card in an sd card reader for reading on a Windows machine - it will hunt the first partition, and if it's not FAT, then Windows won't see it (if the FAT partition is the 2nd one).
3. Before you go rushing out to buy a high capacity SDHC card to use as a secondary drive, check on the forum as to whether your sdhc card will work (Patriot 8 & 6Gb SDHC cards seem to work for example).

BACKUP USB/SD card first!!!

ASSUMES SD card is on /dev/sdb1 for the sake of these instructions - you'll almost certainly need to check. Assumes card is 4Gbytes.

1. Open up a terminal (CTRL-ALT T)
2. df -h (check the mounted device)
3. sudo fdisk /dev/sdb
4. Press d then 1 (This deletes the first partition)
5. Press n then p (New partition, primary)
6. Press enter (to accept the start block)
7. Type +2G then press enter (to make primary partition 2Gybtes)
8. Now type t then 1 (allows you to set the primary partition type)
9. Now type c followed by enter (sets primary partition to vfat)
10. Next, type n then p (New partition primary) then press enter twice to accept the start and end blocks
11. Now type t then 2 (setting 2nd partition type)
12. Next type 83 (sets 2nd partition to linux)
13. Finally, press w then q to make the changes

1. sudo mkfs.vfat -F 16 /dev/sdb1 (makes first partition windows-based, and FAT16. NB: If you're partition is >2Gbytes, you should type sudo mkfs.vfat -F 32 /dev/sdb1 instead)
2. sudo mkfs.ext2 /dev/sdb2

1. sudo mkdir -p /mnt/sd1
2. sudo mkdir /mnt/sd2
3. sudo mount -t vfat /dev/sdb1 /mnt/sd1
4. sudo mount -t ext2 /dev/sdb2 /mnt/sd2
5. (or eject and re-insert)

At first the file system is own by root you need to change that

1. cd /mnt/sd2
2. sudo chown user:user partition1 (that's my folder name)

Now, when you install software, you should be able to specify installation to /mnt/sd2

I'm not sure how to do that using synaptic, or the EEE software installer, as I don't yet have my Eee (should be arriving next week)