I occasionally run an L1 or L2 mission.
Low level missions (L1 and L2) are awful in what they pay - ISK, standing gains and Loyalty points. I understand that if you have been 'bad' then L1 missions are 'better' than nothing, but they still are undesirable.
I currently have access to L4 missions and for distribution missions these are very easy; My ship has enough cargo for 2-3 of these concurrently (Iteron IV with cargo extenders). The ISK is not as good as trading from buy orders; but even with Margin Trading 4, I am running out of ISK for buy orders before running out of buy slots. As I want standing with lots of corporations (at least for buying and refining ore), Mission running L4's is a good fallback activity.
L4 distribution missions pay - lets call it 200,000 ISK + the same in bonus. L2 missions pay - lets call it 20,000 ISK + the same in bonus. Similar order of magnitude differences occur on both Loyalty points and Standing gain. So why bother with poor rewards?
Connections 4. This skill raises a 0.01 standing to roughly 1.6. It has absolutely no effect on a corporation that has a standing of 0 or lower. This is enough standing to make a difference for refining (my current 'preferred' activity) of roughly 1.3%. On a 10 Million ISK refining of Veldspar, that is roughly 130,000 ISK.
A single L1 or L2 mission of any kind successfully completed gives me the difference between a zero raw standing and a non-zero raw standing, allowing the Connections to do it's 'magic'.
I expect to be refining well into the future at a lot of different systems. If I am at a system collecting ore and I don't yet have any standing with them - I look to see if I can do any missions for them. I might not get a full 'L4' mission bonus out of them this time, but the chances are that if I bought ore here once, I am likely to be back here later buying ore from the same miners.