Yes, you can.
But if you have bought a new computer and will be using it to sync your iPhone with regularly, then you may want to move your iTunes library, your purchases and contacts/notes/bookmarks/calenders to your new computer.
How to move your music to a new computer:
Back up your iTunes library by copying to an external H.D.
Transferring purchases from your iOS device to a computer.
Copy/Export your contacts/notes/calenders from the compatible addressbook from your old computer.
To Sync iPhone With New Mac
1- Quit iTunes on both Macs
2- Disconnect your iPhone from both Macs
3- Open the Home folder
4- Copy iTunes directory from the old computer to the new one
5- Open user library directory and copy the backups from the old computer to the new one
6- Also copy over iTunes Preferences files
7- Launch iTunes in the new Mac up
8- Authorize your Mac to Apple Server
9- Connect your iPhone and sync as usual
If you want to sync iPhone to new windows PC, see the below guide.