The block reward halves ever ~1450 days.  So even the block reward wont drop to below 1 btc until 2032 and in the beginning of 2080 the block reward will be 0.00038147 and since bitcoins are infinite divisibility, there should always be a block reward.
That is not much but that could be worth a few dollars.  It might not be worth running the crazy dedicated rigs that some have now but it might be worth running a normal computer and hoping to get a few extra dollars each year.  This all really depends on the exchange rate at any given time.  If the price dropped to $10 / btc tomorrow and stayed there for a while, you's likely see people shutting down their rigs (those that pay for electric, at least).

The truth of the matter is that the system is more secure the more people are mining.  Right now there are properly far too few people in control of mining and deciding how things work.  Think about what would happen if 3 or 4 mining pools got together and demanded a minimum transaction fee to put a transaction in a block.  Some miners would leave the pools, but if the operators shared the fees with miners, not many would leave.