First off, investments can be only made in any port that is marked "Allied", or in ports that are territory of the investor's nation.
Second, investments can only be made once per visit to a port. Consecutive investments can only be made by use of Request Investment Book or by visiting another port before returning to said port.
Next, Investments reveal upgrades only you can see! Thats right, investments in home country and other countries reveal upgrades at the Shop Keeper and Craftsman, like new clothes and books, etc.. also, development status is a combined effort of all investors, revealing upgrades for everybody. This is the reason that when you go to seville you can build really nice ships.
Lastly, investing gives you lots of trade fame and the amount you can invest increases each time you invest a certain amount of money (see the table below). You can also get court ranks by investing and a nice book (depending on home city) at 1 million investment!
I would always encourage anyone to invest in the town he or she frequents the most. When you are beginning, there is little reason to invest; but eventually start your investing with 20% of your equity.
Below is the list for all items that acquirable after invest, either rewarded or bought.
Another type of "reward" for investing is the ability to buy additional items from various merchants. I will attempt to start a table identifying those items below, and hope that others will contribute.