What language has the largest alphabet?

If by alphabet you mean writing system, then Chinese has the largest, with thousands of symbols representing different words, syllables and concepts.

The word alphabet also refers to writing systems were each symbol represents one sound only, such as our own alphabet (with 26 letters) or the Cyrillic (Russian) alphabet (with 29). The largest true alphabet is probably the International Phonetic Alphabet, as it is intended that there is a letter in it for every possible sound. It is not intended for one particular language, but for writing down the sounds of all languages.

The largest segmental script is probably an abugida, Devanagari. When written in Devanagari, Vedic Sanskrit has an alphabet of 53 letters, including the visarga mark for final aspiration and special letters for kš and jñ, though one of the letters is theoretical and not actually used. The Hindi alphabet must represent both Sanskrit and modern vocabulary, and so has been expanded to 58 with the khutma letters (letters with a dot added) to represent sounds from Persian and English.

The largest known abjad is Sindhi, with 51 letters. The largest alphabets in the narrow sense include Kabardian and Abkhaz (for Cyrillic), with 58 and 56 letters, respectively, and Slovak (for the Latin alphabet), with 46. However, these scripts either count di- and tri-graphs as separate letters, as Spanish does with ch and ll, or uses diacritics like Slovak č. The largest true alphabet where each letter is graphically independent is probably Georgian, with 41 letters.

https://en.wikipedia.org/wiki/Alphabets#Types

The Khmer alphabet is the largest alphabet in the world (Guinness Book of World Records, 1995). It consists of 33 consonants, 23 vowels and 12 independent vowels.

http://everything2.com/index.pl?node=Khmer

In Chinese writing, however, there are no letters and there is no alphabet. The writing system consists of a large number of symbols used to directly represent words regardless of their value.