For the benefit of others (I think TBS and Oatman seem to know the score
Euribor is a contract based on 3 months interest rate futures. As you have pointed out - the front month doesn't move a great deal ('cos there's not too much chance of anything interesting happenign to Euro rates in the near term).. If you want to have a punt outright try the 'red' months (next years expiries) they move more.
Generally the guys trading Euribor have to employ other methods to consistently make a buck...
A lot of the Trading Arcades full of ex-LIFFE Locals trade Euribor and the £ equivalent Short Sterling. It's main use is for hedging of interest rate risk for commerce/financial institutions but its not a bad tool to play with if you know the rules, it's liquid and it goes up and down.
Short Term Interest Rate contracts like Euribor have multiple expiries - as well as the Jun03 Future (front-month) it also trades out about 4-6 years in quarterly expiries. The Euribor is liquid in about the front 8 expiries.. Jun, Sep, Dec 03, Mar, Jun, Sep, Dec 04 etc etc..
The main strategies we're talking here are calendar spreads - the difference between Jun and Sep for example is the 'jun/sep spread' As all the expiries on Euribor represent different points along the yield curve they are correlated and as such the differencials between the expiries are in a state of flux. Spread traders will look along this curve (usually in Matrix form if you use J-TRader) and look for arbitrage opportunities in the spreads. It's possible to trade the spread as a single product and also in its component expiries - you can buy jun/sep with one click (long jun.short sep) and you can also try to enter or exit a position by trading the separate jun and sep contracts ('legging the spread').
There are a few other ways of making money - arb'ing Euribor vs. 2 Year Euro Bonds (schatz) for example .. i can imagine this all sounds very alien and complex for the more Index focussed amongst you - to make much money out of this you really need to play quite big or trade constantly. I find it too slow and eyesight intensive personally so stick to the Eurex Bund which moves for the same reasons (int. rates) but is a bit more volatile......