Yep, high contrast scenes, harsh light, speckling shade under trees, etc. -- it's quite a challenge. I've been doing it a lot lately. My best advice is lowered expectations, resourcefulness and lots of post-processing.
Different types of events can have different challenges. In situations where you have some control, you can ask people to move for optimal lighting/background and such. Sometimes you can move objects, most time not. If you want strictly candid shots, you're at the absolute mercy of the elements most of the time. Often it's best to watch the overall event and see where the best setting is -- then set up there and use that as your little "studio." That can take some discipline when a lot is going on all over the place.
If you can pose people, bring along a simple umbrella. Lots of color in an umbrella can be used both as sunshield and background color. A light/gray umbrella can be used for simply diffusing the light uniformly.
Generally, when doing scenes, there's little choice but eval metering. If I'm going for head shots, I'll use spot metering and do as much as I can to fill the frame with the person's head. I also tend to slightly underexpose and use selected fill light in post. Oh, and don't forget a lens hood.
Someone mentioned fill flash. That's always an option in the right situation. I tend to use it rarely -- once or twice in an 800-shot event a couple of weeks ago.
If you have control of time, use it. Where events go on all day, get there early and use better light, or be there late. Sometimes, there isn't a choice -- the July 4 parade here on Wednesday starts at noon. Shooting the vehicles in the parade on the street, I'll need a polarizing filter against glare. To get the people on the sidelines, that filter will just cut down my shutter speed. It's all compromise.
As I said in the beginning, lowered expectations can alleviate some of the frustrations.
Best to remember the old "Dirty Harry" movie advice -- a man's gotta know his limitations.