Note: Excel has several built-in data validation rules for numbers. This page explains how to create a your own validation rule based on a custom formula.
To allow only numbers in a cell, you can use data validation...

To test a cell to see if it contains one of many strings, you can use a formula based on the SEARCH, ISNUMBER and SUMPRODUCT functions. The formula in C5, copied down, is:
=SUMPRODUCT(--ISNUMBER(SEARCH(things,B5)))...

To check a cell for one of several things, and return the first match found in the list, you can use an INDEX / MATCH formula that uses SEARCH or FIND to locate a match. In the example shown, the formula in C5 is:
{=...

To filter data to include only records where a column is equal to one of many values, you can use the FILTER function together with the ISNUMBER function and MATCH function. In the example shown, the formula in F5 is...

To count cells that do not contain many different strings, you can use a rather complex formula based on the MMULT function. In the example shown, the formula in F5 is:
{=SUM(1-(MMULT(--(ISNUMBER(SEARCH(TRANSPOSE(...

To get the position of the first match that does not contain a specific value, you can use an array formula based on the MATCH, SEARCH, and ISNUMBER functions. In the example shown, the formula in E5 is:
{=MATCH(FALSE...

If you want to test a cell to see if it contains all items in a list, you can do so with a formula that uses the SEARCH function, with help from the ISNUMBER, SUMPRODUCT, and COUNTA functions.
Context
Let's say you...

To count the number of cells that contain certain text, you can use the COUNTIF function. In the generic form of the formula (above), rng is a range of cells, txt represents the text that cells should contain, and "*"...

To categorize text using keywords with a "contains" match, you can use the SEARCH function, with help from INDEX and MATCH. In the example shown, the formula in C5 is:
{=INDEX(categories,MATCH(TRUE,ISNUMBER(SEARCH(...

To test if one of several values exists in a range of cells, you can use a formula based on the SUMPRODUCT function. In the example shown, the formula in cell D5 is:
=SUMPRODUCT(--(rng=B5:D5))>0
where "rng" is the...

To allow only unique numbers in a given range, you can use data validation with a custom formula based on the AND, ISNUMBER, and COUNTIF functions.
In the example shown, the data validation applied to B5:B9 is:
=AND(...

To filter a data in an array formula (to exclude or require certain values), you can use an array formula based on the IF, MATCH, and ISNUMBER functions.
In the example shown, the formula in H5:
{=COUNT(IF(ISNUMBER(...

To filter data to include data based on a "contains specific text" logic, you can use the FILTER function with help from the ISNUMBER function and SEARCH function. In the example shown, the formula in F5 is:
=FILTER(...

To allow only values that contain a specific text string, you can use data validation with a custom formula based on the FIND and ISNUMBER functions. In the example shown, the data validation applied to C5:C9 is:
=...

If you have a list of things (words, substrings, etc) and want to find out which of these things appear in a cell, you can build a simple table and use a formula based on the SEARCH function.
Setup
Suppose you have a...