Here are several organizations and coordinated efforts coming to the aid of Texans:

The American Red Cross is encouraging people to donate money on its website or to text 90999 to donate $10. The organization is also asking for volunteers. http://www.redcross.org/hp/harvey2
Other organizations include the Salvation Army http://salvationarmyhouston.org/, Samaritan’s Purse and Heart to Heart International.
The crowdfunding website Global Giving https://www.globalgiving.org/projects/hurricane-harvey-relief-fund/ is trying to raise $2 million to provide “food, water, and medicine in addition to longer-term recovery assistance” to Harvey’s victims.
The crowdfunding service GoFundMe also has highlighted stories of people who are suffering as a result of Harvey.https://www.gofundme.com/raise-funds/hurricane-Harvey
The South Texas Blood & Tissue Center and Texas-based Carter BloodCare (1-877-385-724) are accepting donations https://www.donatingforlife.org/index.cfm?utm_source=website&utm_medium=locations&utm_campaign=11.23.15-dfl-locations-page-website-find-a-blood-drive-link .
Several organizations are offering aid to displaced pets, including Dallas Animal Services http://dallascityhall.com/departments/dallas-animal-services/Pages/default.aspx and the SPCA of Texas https://www.spca.org/news_hurricane-harvey.
And the Texas Diaper Bank is assisting people with small children http://www.texasdiaperbank.org/ .