You certainly can do without a controller. A number of vendors either provide management software with the purchase of the AP or have products that are designed to run without one. You can choose from Cisco, Aruba, Aerohive, Meraki (now Cisco), Ubiquiti and quite a few others (supposedly Meru has a solution soon to launch as well) for solutions that work without a controller.
As for single SSID or multiple, that is really up to a design choice, but generally speaking you would want to only provide one for roaming if you do mobile computing. Wireless clients have been getting better about making good choices when presented with multiple wireless access points, with some notable exceptions (Apple devices seem to still have some issues periodically).
If mobility isn't a concern and you are largely dealing with nomadic (i.e. they may move, but are used almost entirely in one position)or stationary clients, then you can balance your clients in several ways with unique SSIDs. However managing the clients and educating users can be troublesome if you don't put some thought into it.
Controllers largely help with the management, reporting and coordination (and sometimes troubleshooting) of the wireless network. While they are nice to have, they are by no means essential for general wireless. If you are looking to do something more complex or that requires a higher class of service (such as wireless-VoIP), then you should look into a controller based solution.