You don't mention what you wish to use them for. Bread, veggies, etc? That will affect the flavors you choose to put in the butter. Also, there's your personal flavor preferences--do what you like! There's savory butters and sweet butters (though I'm guessing you want savory since you're talking garlic or shallots).

I'm a fan of garlic chives and onion chives when you're talking veggies (this time of year, it's corn and beans for us). Parsley will do a nice fresh green flavor that goes with pretty much anything. For my preference on butters, I go with the stronger flavored herbs (basil doesn't do much for me in a butter) such as the chives, or sage if I'm looking more for bread. I tend not to mix too many flavors--I can always use more than one kind if I want a really complex flavor.

Baloonflower mentioned: It depends of taste and preferences. Bu here alist :

-- dills -- mint --- tarragon --- summer savory -- lemon balm.

I personally use some those in yogurt dip. (use Greek Yogurt)
Plus garlic and shallot.

Balloonflower, I use the butters for garlic toast, to swish in a soup, whisked into a pan sauce, to finish veggies or on a baked potato and on steak. I guess the question is more along the lines of what works together.

Seysonn, I make a yogurt sauce too, here it is normally mint, garlic and lemon juice. More herbs and some oil if I want it to be a salad dressing.

Any herbs usually used in savory dishes would work, depending of course on your preference. See the link for some savory herb suggestions.

FataMorgana

Here is a link that might be useful: Savory herbs

You can go along the lines of what herbs you may add if you didn't have a compound butter. All of these are on top of your garlic and shallots.

Garlic toast some parsley, and I would go with either dill or sage depending on your preference. (ever had a sage browned butter?)

Potatoes and soups, I would go with dill and chives. You could add a little thyme if that's your thing. Same would go well on veggies. If you use chives, maybe skip the shallots, as that would be a lot of onion flavor. Marjoram, or if you like anise flavor, some tarragon could go as well.

For steaks, I would consider some finely chopped rosemary, some pepper (and red pepper flakes if you like a kick), and maybe a little lemon verbena or lemon thyme (or lemon juice or zest). Ever had an Italian style steak?

Fresh herbed butters are wonderful. However, freezing changes the flavor of herbs and so you may want to do some small scale experiments.