I have a bunch of apps that I downloaded to my iPad and am finally able to sync to my computer (it was being fixed), but now, if I sync my iPad to my mac, it wants to delete all the apps I have bought and am currently using. iTunes wants to replace all my iPad apps with my iPhone apps.

Is there a way to back up all of my apps without having to sync and lose all my apps and data?

When you get the erase/sync dialog, there should also be a Transfer Purchases option. Choose that. If you do not get that option, cancel out of the dialog, right click on the iPad in he Devices list and choose Transfer Purchases. Alternately you can select Transfer Purchases from. . . under the File menu.

When it finishes (this may take quite a while, depending on how much stuff you have on the iPad) make sure all your stuff got transferred. If not try the Transfer Purchases option again. On rare occasions, or when it gets interrupted, not everything will get copied.

That should put an end to the dialog about erasing your iPad.