When appropriate, I bring food as a gift instead of cash or items. This has the benefit of being generally cheaper (if I make it at home) and a consumable so I can keep bringing these items for each party, with the same people, and it is still welcomed.
For baby showers, I make freezer dinners for the new parents, like frozen lasagna or chili or something that I know they enjoy. For going away parties, I make a batch of their favorite cookies that can be eaten on the go.
Kid's birthday parties are another beast entirely. I don't have kids, but from my own experience as a kid, this is a situation where you just have to suck it up and get the birthday kid a present. Kid's wont appreciate a frugal, practical gift the way an adult friend would.
If all else fails, evaluate whether it is necessary for you to attend all these events. Maybe prioritize them by importance. I'm sure there are a few that you wouldn't be missed at. Especially, if I'm reading this correctly, birthday parties for coworkers children. Yeah, not necessary at all, I'd just be unfortunately busy that day and couldn't attend.