Rivers are considered holy in the Sanatana Dharma. The Nadi-Sukta in the Rig-Veda (10/75/5-6) praises the rivers.
The Yogini Tantra says
Mahamaya Kundalini resides in the world taking the form of rivers.(18th patala, Ref. Omkarnath Rachanavali, vol.9, page 103).
While doing any formal worship, the water to be used in worship has to be purified by the 'Jala-Suddhi mantra' compulsorily and the mantra invites tye rivers Ganga, Yamuna, Godavari, Sarasvati, Narmada, Sindhu and Kaveri to appear in the water to purify it.
There are many well-known hymns dedicated to the rivers like Ganga, Yamuna and Narmada in sanskrit. The glories of these rivers have been mentioned in the different puranas also.
Bathing in the river is known as the 'avagaahana snaana' which is considered as highly meritorious at auspicious times, as mentioned by Rickross in his comment. Bathing in the ganges in glorified in the Yogini-Tantra as:
One shoulde bath in the ganges at any time : during day or night or evening or midnight. It destiys all sins. (Ibid. page 106-7)
One can read 'Sri Sri Ganga Mahimamrita', 'Sri Sri Narmada Mahimamrita' by Sri Sitaramdas Omkarnath and hymns like Ganga-Stotra,Yamuna-ashtakam and Narmada-ashtakam etc available in various books of hymns like Stavakusumanjali and Stavananjali published by the Ramakrishna Mission, In our culture, rivers are referred to as 'Mother' and India is called a 'Nadi-matrika' country.
This a small stotra written by BhagvatpAd Adi shankrAchArya praising Ganga and it's nirmala water.
Please note that this Kumbha Snana was initiated by Adi Shankara himself. Rivers are highly respected in Hinduism equal to that of mAtA. There are stotras praising Ganga written by Shri Valmiki, Shri Vyas, Goswami Tulsidas ji and many other great Saints. Also, there is another stotra by Adi Shankara. Just go through the above stotra and you'll get your answer. Har Har Gange. Jai SiyaRam.