A good example would be heating a tin can of water using a Bunsen burner. Initially the flame produces radiation which heats the tin can. The tin can then transfers heat to the water through conduction. The hot water then rises to the top, in the convection process.
The atmosphere would be another example. The atmosphere is heated by radiation from the Sun, the atmosphere exhibits convection as hot air near the equator rises producing winds, and finally there is conduction between air molecules, and small amounts of air-land conduction.
Actually a good electric oven is a great example of all three:
The metal that gets red hot emits light (blackbody radiation);
There is the obvious convection of air in the oven, as you mentioned - though this you'll just feel when opening up the oven for a brief time, as gases are not storing that much energy or transmitting it very well anyway;
And there is conduction of heat, as you can feel when you touch any surface inside the oven.
While maybe not the best examples (as some of then involve more complex physics), you can actually come up with many other examples with more exotic nature: a foundry furnace, lava in contact with sea water, and the Sun. I'll let you figure out those other ones (but all those examples have quite a bit in common).