Read Only Memory - ROM

Mask Rom

Mask Rom use MOS transistor to store words. If there is a transistor, it stores 1, otherwise it stores 0. It is impossibe to change the existence of transistors after it is programmed, thus it is read only.
There is a simplified figure for a 1Kx1b Mask Rom.
And a detailed one,
Read Only Memory - ROM

AND matrix is an address decoder. For a n-bit address, 2n output lines leave the AND matrix. If the ROM memory word has k bits, the OR matrix contains k logical OR circuits. Each output line from the AND matrix selects one word, which is programmed by connecting this line to input lines of OR circuits. On ROM word readout, ones appear on outputs of these OR circuit to which the active line from the decoder matrix has been connected.

The main advantage of mask ROM is its cost. Per bit, mask ROM is more compact than any other kind of semiconductor memory. Since the cost of an integrated circuit strongly depends on its size, mask ROM is significantly cheaper than any other kind of semiconductor memory.(Wikipedia)

PROM

PROM can be programmed once when used. It is a digital memory where the setting of bits is locked by a fuse or antifuse. (Wikipedia)The difference between a basic ROM and PROM is that basic is programmed when manufatured, but PROM is programmed on the field side after manufature.
Read Only Memory - ROM

Once the PROM is programmed, the information written is permanent and cannot be erased or deleted. PROM was first developed by Wen Tsing Chow in 1956. An example of a PROM is a computer BIOS in early computers. Today, PROM in computers has been replaced by EEPROM.

EPROM and EEPROM

EPROM stands for Erasable Programmable ROM, where the infomation written can be erased or deleted.
Read Only Memory - ROM

Presence of a voltage on this gate creates a conductive channel in the transistor, switching it on. In effect, the stored charge on the floating gate allows the threshold voltage of the transistor to be programmed.

If one wants to reprogramme it , one should use UV light to dissapate the stored charge on the floating gate.
Other than erase EPROM by UV light. Electricity can also be used. We call that kind of EPROM as EEPROM.

Flash Memory

Flash memory is a type of floating-gate memory that was invented at Toshiba in 1980, based on EEPROM (electrically erasable programmable read-only memory) technology. (Wikipedia)

Flash Memory is as cheap and compact as EPROM, but can be erased and written by electricity. It is often found in USB flash drives, MP3 players, digital cameras and solid-state drives.

Flash memory incorporates the use of floating-gate transistors to store data.