There are four ways to make a global statement that is historically significant at the Olympics. Athletes protesting, countries boycotting, IOC banning countries and IOC cancelling the event.
Putin has made it illegal to protest at the Olympics in Sochi. It's unclear whether or not a silent demonstration like the 1968 "Power to the People" will be permitted, but it's likely that the athletes will have a difficult time in Russia during their stay if they step out of line.
Countries can boycott for a variety of reasons that all point to disagreeing with other countries' behaviours. There hasn't been a boycott by a country in 25 years (North Korea in 1988).
Countries can be banned for violating sections of the Olympic charter, which Russia has done (despite their assertions that they haven't). If the IOC wants to make a truly powerful statement, they can ban Russia from participating as the host country. This would probably lead to Russia disallowing the Olympics in Sochi, but that's a tough decision for them because it generates a huge amount of commerce.
If the IOC feels that it's too late to move them, then this round should be canceled. There hasn't been an Olympics canceled since 1916 with the outbreak of World War I. Think of the political statement that would make to Putin. You are enacting policies and treating you citizens poorly, and this is how we will stop rewarding you.
Boycotting or cancelling the Olympics is a great hardship for the athletes who have trained for four years and, indeed, most of their lives for this opportunity to compete on the world stage. But I think it's the best way to economically and politically say, "You are wrong."
Since the countries won't cancel or boycott these Olympics, the next best solution is to boycott the sponsors. Protest with your bucks. I am boycotting the 2014 Sochi Olympics sponsors for the duration of the Olympics. Some sponsors won't notice (Omega, ATOS), but there will be dollars speaking for several sponsors.
To do it right, I have to boycott my beloved Dr Pepper, which is produced by Coca-Cola in the UK.
The toughest one is probably P&G brands, because they have products all over the place, but it's going to be worth it to me to say they are wrong to sponsor this sports. We'll be avoiding MEXX, Bounty towels, Puffs tissues, Duracell, Mr. Clean, Crest and Oral-B. These are all brands we use weekly in the house and need constant restocking. But I'll be using alternatives for the next month, and if I like the alternatives, it will be a permanent change.
What products do you use? Can you give them up for a few weeks to make a point?