How is it not arbitrage that EURIBOR (EUR) is around -0.5% and LIBOR (USD) is around 0.5%? Why can I not borrow $1B of EUR at EURIBOR (pays me 50bps per year), convert it to USD (also pays me 50bps per year), lend it out at LIBOR, and collect a 1% spread? Am I missing somethign obvious?
EURIBOR
and LIBOR
Because of exchange rate and uncovered interest rate parity (UIP). By the UIP the following relationship should hold between nominal interest rates and exchange rates:
$$ (1+i_{t}^$) = \frac{E_t(S_{t+1})}{S_t}(1+i_{t}^€)$$
In short, the ratio of expected future nominal exchange rate ($E_t(S_{t+1})$) and current nominal exchange rate ($S_t$) should make the interest rates in US ($i^{\\\$}$) and Eurozone ($i_{t}^€$), equivalent eliminating any arbitrage opportunities.  If the equality above would not hold, then there indeed would be an opportunity for an arbitrage, but as soon as people would take advantage of the arbitrage opportunity trading on forex markets would move exchange rate to the proper position. You can learn more details on intuition behind UIP in Copeland Exchange Rates and International Finance.
In real life the above equation will sometimes be violated but empirical evidence shows trading typically eliminates arbitrage opportunities very fast. Usually within hours or days, or few weeks at the most save for some special circumstances (see discussion in Nelson International Macroeconomics and Finance in first chapter).
In addition, to the above mentioned UIP which may not always hold there is also related concept of covered interest rate parity (CIP) where expected future exchange rate is replaced with value of futures for the exchange rate and thus given by:
$$ (1+i_{t}^$) = \frac{F_{t}}{S_t}(1+i_{t}^€)$$
When it comes to intuition and mechanism of the model there is not much difference between UIP and CIP but evidence shows CIP is being violated less frequently (again see the Nelson reference above). This is precisely because value of future contracts is easier to measure and thus any possible arbitrage will closed much sooner or even prevented altogether by movements in price of futures.