I would like to backup my data to two external drives. That way I would like this to work is that both disks should have have a full backup of my internal disk. Is this the way TimeMachine would work?
I don't think time machine will backup to two separate disks simultaneously, but I can give you my backup solution:
Time Machine to external drive. Easy and I don't ever have to think about it. Just plug it in and BOOM! backup.
Second, bootable backup to a second external drive using CarbonCopyCloner. This one runs on a schedule and it's a free program.
Dropbox. I have the 50gb account, and I store all of my current projects, important documents, and anything else i may need at any time, whether I'm in front of my Mac or not. Using the Dropbox iPhone and iPad apps along with the web interface, I can always get to important files when I need to.
Finally, I use Arq to backup a copy of my library folder to an Amazon S3 bucket. This one is a paid app, but worth it because I'm paranoid and it makes me feel comfortable that even if both of my backup drives fail, between the S3 Library backup and my documents on Dropbox, I can recover from a disaster quickly and with minimal hassle.
You might consider 1 Time Machine disk and 1 disk that is using CrashPlan. The CrashPlan disk can be offsite too.
This has always worked well to cycle drives in to back up your files to more than one place. Mountain Lion can now track two drives at once, so you don't need to keep setting up a new preference, but I have used this for several machines since day one with Time Machine.
Before Mountain Lion, you needed to enter the Time Machine preference pane and select each drive as you connected the new drive to break the expectation that the system should back up to a drive that's now not mounted.
I have seen this work well for using multiple drives and cycling them manually for weekly, monthly and more sparse rotation schedules including if you place a drive off-site or keep one drive mostly in a fire safe (in a waterproof container) for enhanced protection in case of a fire (and/or flood).
With Mountain Lion, you can tell the system to alternate between two drives so a simple A/B rotation means you can set it and forget it. If both drives are connected, each backup will alternate between drives, but if only one drive is connected, all backups will go to that drive. When you reconnect a drive that has missed several backups, it's only an hour or two away from being updates.
Of course - you now have two (or more) locations to find any one instance of a file, but again, the longer a file lives - the higher chance it's on both drives. Files you download and delete could only get backed up to one drive, but if a file sits on your mac long enough to get saved to both drives, you'll have at least two copies of it should you delete it and need a recovery later.