Are there poems in Chinese that rhyme?
This question really surprises me. Since you mentioned 李白 and 杜甫, clearly you were talking about classical Chinese poetry. Classical Chinese poetry is so into rhymes and rhythms that it is almost unhealthy. There are volumes of books written on rhymes and rhythms of classical Chinese poetry. Asking 'Are there poems in Chinese that rhyme?' is like asking 'Does Facebook have users?' or 'Does Bill Gates have money?'

Many ancient poems do not rhyme today because Chinese pronunciation has undergone many changes over time. They did all rhyme at the time written.

Here is an example of a poem in which every sentence rhymes. This kind of poem has a special name called 柏梁体. This poem I'm quoting rhyme at the end of every sentence even today:

曹丕《燕歌行》

秋风萧瑟天气凉，
草木摇落露为霜。
群燕辞归鹄南翔，
念君客游多思肠。
慊慊思归恋故乡，
君何淹留寄他方？　
贱妾茕茕守空房，
忧来思君不敢忘，
不觉泪下沾衣裳。
援琴鸣弦发清商，
短歌微吟不能长。
明月皎皎照我床，
星汉西流夜未央。
牵牛织女遥相望，
尔独何辜限河梁。