How much RP can I get at no cost

At level 3, new summoners get a 400 RP bonus. Are there other ways to earn RP using such bonuses or promotions like the Tristana and Alistar free promos?

The only RP you'll get for free is the 400 RP upon hitting level 3. Plus the 450 RP Riot usually hands out in December as a Christmas gift. The new recruitment program also rewards heaps of RP and IP.

The refer-a-friend program can get you 975 RP (and 5000 IP). Riot has cracked down on people making 10 alts and grinding them up to level 10 just for the free stuff, but it's a bit of a no-brainer if you happen to know 10 or more people who don't (yet) play LoL :)

For more info:

http://leagueoflegends.wikia.com/wiki/Refer_A_Friend