Is it possible to read a microSD card (on a breakout) through the USB port on the arduino? or perhaps another USB port I could attach to the breakout? Basically, I would like to read data off the card with my laptop without having to go and remove it each time!
It would be very useful, but afaik this is not possible, since the Arduino sketch you write communicates to the PC via the serial interface only.
The IDE/Arduino driver can use the USB to write your sketch and use the USB for communicating, but for sketches the USB (as direct medium) is not possible.
The SD card will not show up as a specific drive/map/folder on your PC.
Since you want to read the SD card, write in your sketch code to transmit the file(s) you want to send to the PC, to transfer them by UART, and on the PC write a program that reads the serial port and processes it.
In general that's possible. But you can't read the sd card through the arduino's usb port. Instead you have to read the sd card via another protocol, e.g. SPI (look for the apropriate library) and send it to the pc via serial. You'll need software on the pc side to write the content that was read from the arduino to a file.
Take a look at the SD card tutorial to see how to read it.
It can't be done with an Arduino, but it can be done with other microcontrollers. You need a microcontroller with a direct USB ("native") connection plus a USB stack that is capable of acting as a USB Mass Storage Device. Something like the Teensy or chipKIT series of boards can do that.
Then you can write software that will, on command, detach the SD card from your normal sketch operation and re-attach it to the MSD device in the USB stack. You can then read and write to the SD card (though your sketch otherwise cannot access it) as much as you like - then "unmount" the MSD device and detach the SD card from it, at which point your sketch is then free to re-attach itself to the card and start using it again.
Note that the important thing here is that only one functionality can work at a time - either you can read and write the files on the card with your sketch, or you can export the device through MSD. Never both. That way leads to filesystem corruption and loss of data.