What are the benefits of raising standing with a corporation or faction? And at what level standing are they available to you?
Having high faction standing with an Empire faction allows you access to that faction's Factional Warfare militia at 1.0. Beyond that, standings with the relevant Empire faction (Amarr Empire for Imperial Navy, for example) can be used as a substitute for corporate/personal standings when looking for an agent to run missions for. This allows players with high faction standing to choose nearly any agent in friendly space to run missions for.
High standings with certain corporations (Lai Dai, Carthum Conglomerate, and other research corporations) allows players to use R&D agents, who provide Research Points on a daily basis that can be used to purchase datacores. These can be sold to inventors for a decent passive income in the range of 30M/month for players with good skills.
Lastly, high faction standings with an Empire faction allow players to place POSs in that Empire's high security space. These POSs are generally more secure than POSs in low security or nullsec, due to the restrictions on capital ships entering high security space. This makes them perfect for small research/invention corporations, as labs can be anchored at these towers in order to bypass the long queues at NPC Outposts.