What are Solidity's basic primitive types, and what does each hold?

Question

Accepted Answer

bool (true/false), uint (unsigned/non-negative whole number), int (signed whole number), address (a 20-byte account/contract address), plus bytes (raw byte data) and string (text).

Type
Holds
Example

bool
true or false
bool hasNumber = true;

uint
non-negative whole number
uint256 favoriteNumber = 5;

int
positive or negative whole number
int256 temp = -5;

address
an account or contract address
address owner = 0xAb...;

bytes
raw low-level byte data
bytes32 data = "cat";

string
text (secretly an array of bytes)
string name = "Patrick";

uint is short for uint256. A string is really just a bytes array restricted to text — a short literal like "cat" can be auto-converted to a bytes value. Types exist to tell the compiler what each variable is and how much space it needs.
Go deeper:

Solidity docs: types — the full reference for value and reference types.
 Solidity (Wikipedia) — an overview of the language and its design.

Type	Holds	Example
`bool`	true or false	`bool hasNumber = true;`
`uint`	non-negative whole number	`uint256 favoriteNumber = 5;`
`int`	positive or negative whole number	`int256 temp = -5;`
`address`	an account or contract address	`address owner = 0xAb...;`
`bytes`	raw low-level byte data	`bytes32 data = "cat";`
`string`	text (secretly an array of bytes)	`string name = "Patrick";`