What is the difference between OSPF and RIP?
http://livinginternet.com/i/iw_route_igp_ospf.htm
The main difference between OSPF and RIP is that RIP only keeps track of the closest router for each destination address, while OSPF keeps track of a complete topological database of all connections in the local network.
This was the first search term google returned when I pasted your question there.
To more closely answer your question, if you're maintaing a very small network, RIP is fine, if you go beyond 3 or 4 routers then perhaps look at a more advanced routing protocol like OSPF.
RIP is more common to the internet where you cannot know the topology of the entire network and what devices are neighboring you. For example you connect to the ISP but you do not know about your neighbors or rest of ISP connection. RIP is therefore simpler to use in a limited network. OSPF is used in larger networks in larger orgnizations where topology and devices can all use OSPF (most of them) but there is no way to manage so many devices (imagine defining routes in every system when you have 100s or 1000s). So OSPF helps here by handling outage to a certain extent.
RIP is more available though. OSPF if I remember correctly was proprietary protocol and most likely found in Cisco devices
edit: RIP is older than OSPF and said to be slower but much simpler in design
RIP takes up bandwidth by broadcasting the entire route table update every 30 Seconds. OSPF and EIGRP does not they only update when a change in the route table occurs. RIP is only good for 16 hops and anything pass that you get Network is unreachable.