To find the ADRs with the largest market cap and best yields, I ran the stock screener with the following conditions:

Stock Type = ADRs
Exchange = NYSE
Dividend Yield = 5%+
Market Cap = $100B+

The search resulted in 6 stocks noted below:

Company: Royal Dutch Shell plc (RDS.A)
Country: U.K.
Sector: Oil
Dividend Yield: 6.48%

Company: BP plc (BP)
Country: U.K.
Sector: Oil
Dividend Yield: 6.57%

Company: TOTAL S.A.(TOT)
Country: France
Sector: Oil
Dividend Yield: 5.95%

Company: Banco Santander, S.A.(STD)
Country: Spain
Sector: Banking
Dividend Yield: 5.35%

Company: Telefonica S.A (TEF)
Country: Spain
Sector: Telecom
Dividend Yield: 5.47%

Company: Vodafone Group Plc (VOD)
Country: UK
Sector: Telecom
Dividend Yield: 8.04%

Just one bank from Europe is in this list. The rest of them are either oil or telecom companies. These two sectors have remained strong during the credit and crisis and have since rebounded nicely. Telecoms for example have stable revenue generating traditional land line business. Other areas such as wireless, voice, data, etc. add more income. Similarly oil companies pro fitted heavily last year when crude oil prices reached stratoshperic levels. Royal Dutch Shell, BP and Total are multinationals with operations in many countries.