Wiimote-less games:
SSBB can be played using gamepad only. Also Mario Kart Wii, and definitely some others I've never heard of, much less played.
Wiimote cursorless games:
NSMB Wii does not use cursor much, but requires tilt, which should work OK, depending on how it's mapped. I recommend Super Mario World-style mapping, with tilt assigned to triggers or an analog stick, depending on whether your controller has it or not. Assign shake to right-button, but note that it will constantly spinjump if you hold it down, unlike Super Mario World.
Wiimotes?? :
Cheap Wiimotes have poor compatibility with Dolphin. Currently, the Wiimote code is rather wonky and only kinda-sorta works properly with official remotes. Unofficial Wiimotes may work, may be unreliable because of different timing that works with Wii but not Dolphin, may have broken features, or fail entirely.
Now, Wii Remote Pluses do not work well with Dolphin either, as they fail to connect unless you have the Toshiba stack installed or something something. The Toshiba stack only officially works with Toshiba bluetooth devices and will have a 30-day expiration, resettable by reinstalling. The normal Microsoft stack supports older Wiimotes, just not Pluses. Not sure how well third-party works with either stack.
SSBB can be played using gamepad only. Also Mario Kart Wii, and definitely some others I've never heard of, much less played.
Wiimote cursorless games:
NSMB Wii does not use cursor much, but requires tilt, which should work OK, depending on how it's mapped. I recommend Super Mario World-style mapping, with tilt assigned to triggers or an analog stick, depending on whether your controller has it or not. Assign shake to right-button, but note that it will constantly spinjump if you hold it down, unlike Super Mario World.
Wiimotes?? :
Cheap Wiimotes have poor compatibility with Dolphin. Currently, the Wiimote code is rather wonky and only kinda-sorta works properly with official remotes. Unofficial Wiimotes may work, may be unreliable because of different timing that works with Wii but not Dolphin, may have broken features, or fail entirely.
Now, Wii Remote Pluses do not work well with Dolphin either, as they fail to connect unless you have the Toshiba stack installed or something something. The Toshiba stack only officially works with Toshiba bluetooth devices and will have a 30-day expiration, resettable by reinstalling. The normal Microsoft stack supports older Wiimotes, just not Pluses. Not sure how well third-party works with either stack.