I guess it really depends on the Action Sequence or roll..here are some general examples I've used:

1) Rescue innocent bystanders (1 Raise / Bystander)

2) Protect priceless/valuable items (1 Raise / Item)

3) Notice an important thing about the scene (1 Raise / "notice") - This can include an important bad guy sneaking away, some weakness in the target they are fighting, guards are coming to round everyone up, etc.

4) Gain some ground in a chase; Slow down a pursuer in a chase

John

The only I can think of are one of my players using them to add interesting things to the fiction (mostly during what I do as dramatic sequences). He invoked the sign of his former eisenor company on crates in a forest camp. Later he saw in the house of a lone widows, through small crack on the door, an old zweihander. He deduce she was or knew a mercenary and used this to convince her of hosting him. The other used an opportunity during a "please ghost of a fighter help me" risk to invite him inside his body (and he is now possessed). While deciphering a coded letter from a curonian agent, I gave them opportunity to learn more about the writer (he was in a hurry, the ink is still pretty fresh etc.). Some combat related (but not much, because they are all duellist and maneuvers are strong enough to risk being less effective with an opportunity).

Noticing things in a scene.

Using Big stuff for things (a tapestry to create a safe passage for some turns during a fire, a very big oak door to ram a Montaigne nobleman).

Rescuing people or objects.

Slipping past guards.

Befriending people (besides getting them to tell you stuff and or give you stuff).

I have had one player set up an opportunity for another by declaring that they were going to manuever a Villain into a specific position so a non-duelist could hit the villain with some rigging and tie him up.

My players, as yet, are still used to traditional 'move and roll,' though they are slowly getting the hang of it. Last game was the first game in a half dozen that someone chose to fail.

Things I offered are an opportunity to distract someone so another player could slip by unnoticed (without having to change approach), snatching a letter from a coat before the person they were fighting fell off the coach, the chance to impress a specific woman at a fete.

But I admit, opportunities on the fly are one of my areas most in need of improvement. So, more examples are always loved. 
 

- Grab the enemy's pistol/sword from their belt
- Call out to an ally/a warning to another
- Notice a minute detail that proves useful
- See a way out during the fight
- Spot a dropped weapon, item

I tend to see them as "something added to your action" and remind them paying for an Opportunity is like doing a second action that moment, reducing your remaining Raises for anything else for the rest of that Round.