Forecasters said Ike, which has already killed at least 80 people in the Caribbean, could strengthen into a massive Category 3 storm before slamming into Texas or Mexico this weekend.
Residents in Texas and northern Mexico braced for a weekend hit from Ike.
Given its current trajectory, Ike potentially could hit Texas Saturday, reported CBS Early Show weather anchor Dave Price, who added that the storm's intensity is still "too hard to predict."
Some 1.2 million people - more than a tenth of Cuba's population - sought refuge from Ike, which killed four people and shredded hundreds of homes as it barreled across the island.
Winds howled and rains lashed the empty streets of Havana as towering waves broke over the seaside Malecon promenade, devoid of the bustling crowds of Havana residents who normally fish and chat by day and drink and socialize at night. Navigation was banned in Havana Bay, its usually placid surface stirred up by white-capped waves.
Police braved the storm to stop all but emergency traffic in streets littered with branches, rocks and the rubble from crumbling balconies.
The heavy rains soaked the buildings of Havana's picturesque older areas, causing some of the more dilapidated to collapse. Four aging houses on a single block were reduced to rubble when their walls came tumbling down with a loud boom, and work crews labored with heavy machinery in the strong winds to clear the rubble from the street.
Collapsing buildings were reported throughout the city, and more were probable in coming days as the structures dry out and weaken. All of the buildings appeared to have been evacuated, and no injuries were reported.
To the west, reports of damage were still sketchy as Ike moved across the region. Dangerous storm surges were reported along the southwestern coast, which is lined with small fishing villages. State news media said 19 coastal communities were evacuated.
State television said reservoir levels in the western province of Pinar del Rio were dangerously close to overflowing and flooding nearby communities and roads.
Many in the region, where most of Cuba's famed tobacco is grown, were still without power and water after monstrous Hurricane Gustav struck as a category 4 storm on Aug. 30. That storm damaged 100,000 homes and caused billions of dollars in damage, but didn't kill anyone because of massive evacuations.
Cuba evacuated for Ike as well, with hundreds of thousands seeking safety with friends, relatives or at government shelters. Evacuations are not mandatory in Cuba except for pregnant women and small children, but in an authoritarian state, few people ignore the government's advice.
Teresa Tejeda said she was too scared to stay in her shaky, old apartment building, and joined several hundred other elderly people at a government shelter.
"My house has really bad walls and I feel much more secure here," said Tejeda, who is in her 70s.
Police told Niyel Rodriguez, 21, that she had to move to a shelter with her 19-day-old daughter Chanel. She huddled Tuesday with 109 expectant and new mothers and their children in a wing of an Old Havana maternity hospital.
"They came looking for me yesterday and brought me here in a patrol car," Rodriguez said. "I probably would have been scared to stay at home with my little one, and here they take good care of us. They give us breakfast, lunch and dinner and everything we need for the babies."
Officials evacuated about 10,000 tourists from vulnerable seaside hotels, mostly from the Varadero resort east of Havana.
Francisco Camps, operations manager for Sol Melia Hotels & Resorts in Cuba, said no major problems were reported at the Spanish chain's 24 hotels on the island and no guests were hurt. Ike broke some windows and caused roof damage at two of its hotels in the eastern province of Holguin, he said.
Spanish tourists Jose Luis and Avelina Alonso spent the last day of their Cuba vacation in the lobby of an Old Havana hotel. They were getting free meals, but said weather had wrecked their vacation plans.
"We arrived with Gustav and we are leaving with Ike," Jose Luis Alonso said.
State television said four people died as Ike moved across the island, including two men killed removing an antenna from a roof, a woman who died when her home collapsed and a man killed by a falling tree.
Out in the Gulf, Ike was expected to strengthen before hitting the coast in Texas or northern Mexico this weekend.
"When it's out of Cuba it has the potential to become a lot stronger," said Felix Garcia, a meteorologist at the National Hurricane Center in Miami.
However, oil prices closed below $104 a barrel for the first time since early April, in part because traders were betting Ike would miss critical Gulf Coast oil installations.
Mexican officials warned that unrelated heavy rains in the northern part of the country had caused more than a dozen dams to reach capacity or spill over. If Ike brings more rain to the area, evacuations could be needed.
At 5 p.m. EDT, Ike was just off the coast of western Cuba, 90 miles west-southwest of Havana. It was moving west-northwest at 10 mph and its maximum sustained winds were 75 mph.
Meanwhile Tropical Storm Lowell was off Mexico's Pacific coast, projected to cut across the Baja California Peninsula on Wednesday or Thursday and emerge over the Gulf of California near the town of Loreto, popular with U.S. tourists. It had maximum sustained winds of 45 mph, but was expected to weaken before hitting land.