Yes you can, but it is very hard to pull it off. Some advice if you're going to try it:
a) Remember that coastal cities have 1 hex LOS. The enemy can see you coming if you try to land directly in a city.
b) Always, always bring a supporting navy with you. This will be essential to keep your beach-heads supplied.
c) The number of troops you can land simultaneously depends on your transport capacity.
d) Units in transport ships get serious efficiency penalties if they spend a long time transports. Eventually, if they spend way too long in transports they also start to lose hp.
c) Supply is key. Amphibious attacks can only be at full supply on coastal hexes. To go any deeper in land, you'll have to capture a town. The easiest to capture are coastal cities as you can provide supply to your attacking forces, and bombard with your Battle-fleet (Battleship unit). If you succeed in this (which can already be a challenge enough) your forces will still be on half supply as they push in-land, so the defender will have a big advantage.
Basically, if you're considering it, make sure you prepare well, and don't try it on a strong enemy.
So taking Egypt for example. Your best hope would be to try and land from the south with as many troops as you can simultaneously, bringing your navy from the north to support. If you can clear the Suez, try to fortify it and provide your northern and southern units with supply from the sea. Then it would be a case of trying to take Cairo, to restore your full supply. This will be the hardest part in all likelyhood, and might cause you pretty heavy casualties.
Try it if you dare :)