Paris opened higher while Frankfurt, London and Shanghai were little changed and Tokyo retreated.
The House vote sends Trump's case to the Senate for trial. Republicans who control the Senate say they plan to acquit him.
Trump is accused of abusing his office by pressing the government of Ukraine to investigate a potential political rival ahead of next year's presidential election. He also is accused of obstructing efforts by Congress to investigate that allegation.
The outcome will be "greater polarization, and a rapid Senate dismissal of the charges made in the House, and then even greater polarization," Rabobank said in a report.
In early trading, London's FTSE 100 was off 5 points at 7,535.20 and Frankfurt's DAX was up 8 points at 13,229.64. France's CAC 40 gained 0.1% to 5,966.35.
On Wall Street, futures for the benchmark Standard & Poor's 500 index and the Dow Jones Industrial Average were flat.
The S&P closed up Wednesday less than 0.1% while the Dow dropped 0.1%. The Nasdaq composite rose 0.1% to a record.
In Asia, the Shanghai Composite Index closed at 3,017.07 and Tokyo's Nikkei 225 lost 0.3% to 23,864.85. Hong Kong's Hang Seng sank 0.3% to 27,800.49.
Seoul's Kospi was off 2 points at 2,195.56 and Sydney's S&P-ASX 200 lost 0.3% to 6,833.10.
India's Sensex rose 0.2% to 41.636.03 while New Zealand and Singapore also gained. Taiwan and Jakarta retreated.
The Bank of Japan left its short-term policy rate unchanged at -0.1% and its target for 10-year government bond yields at 0%.
The bank downgraded its view on industrial production and said overseas risks are significant, a change from October's statement that they were increasing.
Indonesia's central bank also left its main policy rate unchanged.
Australia reported stronger-than-expected November jobs numbers.
Australian employers added 39,900 jobs following a revised loss of 24,800 in October. Annual growth held steady at 2% over a year earlier.
On Wall Street, the benchmark S&P 500 index and the Dow Jones Industrial Average finished with small losses that left them just below all-time highs.
The S&P 500 fell 1.38 points, or less than 0.1%, to 3,191.14. The Dow dropped 27.88 points, or 0.1%, to 28,239.28. The Nasdaq composite rose 4.38 points, or 0.1%, to a record 8,827.73.
Losses in banks, industrial stocks, household goods makers and technology companies helped pull the market lower. They offset gains in real estate, communication services, health care and elsewhere in the market.
The House vote to impeach Trump, which investors expected, appeared to have no impact on the market.
FedEx was the biggest loser in the S&P 500 after the package delivery giant cut its profit forecast for its fiscal year and reported weaker quarterly earnings than analysts expected. The company cited "weak global economic conditions" and higher expenses.
ENERGY: Benchmark U.S. crude lost 8 cents to $60.77 per barrel in electronic trading on the New York Mercantile Exchange. The contract declined 2 cents on Wednesday to close at $60.85. Brent crude, used to price international oils, shed 9 cents to $66.08 per barrel in London. It added 7 cents the previous session to $66.17.
CURRENCY: The dollar was little changed at 109.56 yen. The euro rose to $1.1127 from $1.1114.