I have Mobil 1 grease in my grease gun. I've had issues with it losing prime and oozing out of the gun, but since I've been storing it with the pressure relieved it has been acting better. I've also learned that you can't use the gun in cold weather or it loses prime (it is just too thick to return to the piston).
I keep looking at other greases, but keep coming back to Mobil 1. Just the other day, I was looking to see if there was anything better for all metal ball joints, and I was not able to find anything with a better 4-ball scar rating (the best test I could find to give an idea of how fast you see wear on metal to metal sliding surfaces).
I see so many people recommending moly grease for places where it makes no sense. Molybdenum disulfide will plate itself onto steel, and can help in a steel on steel sliding connection that is not well greased (it buys you a little protection after the grease is gone), but in most cases the steel is not the part that wears out first (i.e. steel wearing on bronze, or plastic or sintered metal, a hard chrome or nitrided surface, etc.), and in those cases moly can actually accelerate wear and corrosion. The plating action is a big problem on bearings, because it can make a smooth bearing lumpy, and one with a proper fit become too tight. This leads to bearings sliding, and premature failure.
For places where moly is appropriate, I have dry moly that I can add to whatever lubricant I want.
I have silicone dielectric grease, which is used on electrical connections and non-moving o-rings (like seals on headlamp bulbs). I also use this on some brake parts.
Then, I have spray lithium grease, for places where it is just easier to lube with a spray.
Finally, I have tubes of Krytox, for situations where nothing else will do. I find it especially great on sliding o-rings.