I expect it depends on how dirty the food is to begin with, and on what type of dirt (just as the answer to this other question depends on how dirty the floor is), and also on whether the food is subsequently cooked.
This FDA page and this Health Canada page both recommend washing (using identical text).
However, the FDA site says that that's not effective for sprouts:
Rinsing sprouts first will not remove bacteria.
One problem (i.e. the reason why washing doesn't always work) is that pathogens can sometimes get inside the produce: for example, see item 3 of this web page:
What is the evidence of internalization of pathogens into produce and how significant is this?
- Is it a problem with crops other than tomatoes, apples and potatoes?
- What are the best prevention methods?
- Once pathogens infiltrate the product, how long will they survive/grow?
- Can epidemiologically relevant numbers of pathogenic microorganisms infect a field crop via this route?
The same page lists "What is the efficacy of produce washing at home? (Does water remove pathogens from product?)" as a low-priority research area for them.
Page 43 of this 2008 WHO document (on which that previously-mentioned Canadian page was based) says various things including,
Washing in potable or sanitized water typically results in TVC/ACC reductions of 1–2 logs
(CCFRA, 1999, 2002). However, the degree of risk reduction that can be expected from these
current washing disinfection technologies is difficult to quantify in reality (i.e. under non-inoculated conditions) given the sporadic nature of contamination by pathogens.
This quote from the same WHO document implies that washing is more effective for fresh-harvested produce (e.g. from your garden), and less so for older produce:
Owing to practicalities, most industry trials of process water sanitizing agents use naturally
colonized vegetable tissue, which is at the mature biofilm stage and therefore very resistant to
the effects of washing, even in sanitized water. Commercial washing processes in relation to
surfaces for fresh-cut produce are typically within a few minutes of chopping, shredding or
dicing. Such washing occurs before the establishment of the protective extracellular
polysaccharide, yet the washing process does not remove all of the bacteria (Liao and Cook,
2001; Zhang and Farber, 1996; Brocklehurst, 1994; Baranyi, Roberts and McLure, 1993) since
it fails to address the substantial biofilm element of the attached population.
A lot of data is about food safety protocols on farms (how should they manage their manure/fertilizer, for example), and in the commercial processing which follows, before it's delivered to the consumer.