Sure they make $$ if you finance with them and it is always a good idea to just get your best price up front without regard to finance and/or trades, but that is easy to say.
Keep in mind that sometimes a dealer has a rebate for you if you finance. Sooo, if no prepay penalty is involved, take the finance and rebate followed by a quick payoff. Example---Last year GM had a $1000 rebate for those who used GMAC financing. I had planned to pay cash for a car I bought, but I went along with the deal and paid off the loan about 45 days later. Cost to finance--about $145--net of $855 to me.
JP is correct, some rebate deals will require you to finance with the financing arm of the manufacturer. Paying it off asap is the right thing to do.
Also when the manufacturer is offering low finance rates such as 2.9 of 3.9 the dealer is not receiving any finance reserve monies.
Although some manufacturers do kick back a flat fee of about 50 bucks to the dealer for doing the paper work.
Don't worry, no one is going on vacation from the dealership because of your finance money.