I am maintaining a couple of sites who run on CE 1.5.X, and 1.4.X of magento.
Can I just upgrade directly to CE2.X? There won't be any problems?
If you want to upgrade your Magento, you can use this tool https://www.magentocommerce.com/magento-connect/magento-to-magento-migration-tool.html . It supports migrating both versions CE 1.5 and 1.4 to 2.0