That's not good. The integration services are pretty important, and no, there is no other way to access your VM. Most likely you will have to download the VHD from your blob store (use something like Azure Storage Explorer) and boot it locally using Hyper-V (ideally), VMWare or VirtualBox.
If your machine becomes unresponsive to ssh there is usually no recovery path aside from downloading it, fixing it locally, and uploading the VHD back to Azure. There are a number of instructions to follow to configure CentOS for the hypervisor that runs on Windows Azure, so you should make sure you install what you need from this list of RPMs. That list was found via Microsoft's list of endorsed Linux distributions on Windows Azure. The applicable RPMs are most likely the latest WALinuxAgent (as of this writing, 1.3.3), and then each of the subsequent RPMs should be installed as well, although I'm not sure in which order.
If you're running CentOS below 6.2, there may not be any official support for running on Azure, and changes in the past year to the hypervisor Azure uses (the same as in Windows Server 2012 / Hyper-V Server 2012) may make it difficult to run your VM. The key thing, if possible, would be to update your kernel to the newest version for which a backport exists and to ensure you're running the newest possible Hyper-V (hv) kernel modules. If you're running CentOS 6.4 or newer, it looks like the integration components are built in.