Start a very early war with each and every civ that tries to move his spearman/setter to build his cities. Kill the spearman and liberate his settler into workers. Do this without remorse to your continental neighbor and those civs that try to plant cities on your continent. Do this especially if:
1. You feel that there are quite a few civs on your continent.
2. You discern that you can expand fast and early to hold on to one end of the continent.
Don't worry about those civs you get into trouble with. Those foreign(not local to your continent) civs that you do early wars against are the ones closest to you. Those civs at the other end of the world will most like not try to expand on your continent so you'll be on good terms with them. There are a few consequences of this.
Locally:
1. You'll have quite a bloody conflict with your continental rival/s.
2. The civ sandwiched between you and another civ on the same continent (if there is any) will die to your forces quite easily and very early (horsemen and swordsmen era).
3. After the 'middle-man' is toast you'll continue with your bloody war with the other civ who holds the other end of the continent.
4. You will win lots of battles defensively and may produce several GLs to hurry up wonders

. A good offense greatly depends on techs and resources so hold back on totally conquering the continent until you have the numbers and the power. Just build lots of catapults and station them in the border cities.
Internationally:
1. You'll make lots of enemies since you stole a lot of their settlers/workers very early in the game

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2. The other civs that didn't land on your continent (hence on good terms with you) will easily become your allies because they themselves most likely are at war with your enemies(land grabbing).
3. Your foreign enemies will lose all their battles against you since they generally will land very few units on your beaches to be of any threat (just be on the defensive and you'll be okay).
Emotionally:
1. You relieve yourself of the headache of rationalizing if you should keep peace with the settler's owner). Just make war and claim the settler/worker for yourself!
2. You don't feel claustrophobic knowing that you only have very few borders by land.
Against your continental rival, keep the war going infinitely. There is no point going for a peace treaty since you want them to focus on the war. They'll lose a lot of units and you'll gain several GLs. You essentially are milking them while their economy gets screwed trying in vain to build forces to kill you

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EDIT: excessive use of smilies.