I've mostly read classical poems from guys such as 李白 and 杜甫, very nice in their own way, but it made me wonder if there is some form of poetry with rhymes in Chinese.
It would probably be more difficult to write such poems, due to the lack of available syllables, but possible.
Does anyone know of rhyming Chinese poetry?
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。
Note: The previous answer was replaced with this one, see the edit summary for the full explanation of why.
A great poet along with Li Bo (also known as Li Po or Li Bai), was 杜甫 (Dù Fǔ, also known as Tu⁴ Fu³ in Wade-Giles).
You can find works written by him in this page, "Chinese-poems.com"（you can find more authors in this site).
One is this one, for example:
对雪 (duì xuě) - Facing Snow
战哭多新鬼 zhàn kū duō xīn guǐ
愁吟独老翁 chóu yín dú lǎo wēng
乱云低薄暮 luàn yún dī bó mù
急雪舞回风 jí xuě wǔ huí fēng
瓢弃尊无绿 piáo qì zūn wú lǜ
炉存火似红 lú cún huǒ sì hóng
数州消息断 shù zhōu xiāo xī duàn
愁坐正书空 chóu zuò zhèng shū kōng
The scheme for this one is A B C B D E F E
Actually hóng and fēng were/are considered perfect rhymes in Chinese, so the pattern is ABCBDBEB. Especially that it is a lüshi poem, so all eight rhymes must match.
Not literal translation:
"After the battle, many new ghosts cry,
The solitary old man worries and grieves.
Ragged clouds are low amid the dusk,
Snow dances quickly in the whirling wind.
The ladle's cast aside, the cup not green,
The stove still looks as if a fiery red.
To many places, communications are broken,
I sit, but cannot read my books for grief."
