Site search is radically important. Site visitors that use search boxes are more likely to know specifically what they want and are closer to conversion than those just browsing.
For ecommerce site search, it's table stakes to handle plurals and misspellings. Many sites employ autosuggest that help direct customers to successful search results.
One area where even the top online retailers consistently fall down on is handling synonyms. For terms that can be correctly spelled in more than one way, default search dictionaries often don't accommodate "correct misspellings." It's up to your merchandising team to anticipate these and program your search-merchandising rules accordingly.
Finding examples is like shooting fish in a barrel. For instance:
Target: "2 piece bathing suit," "2-piece bathing suit," "two piece bathing suit"
ASOS: "snake skin," "snakeskin"
Best Buy: "headphones," "head phones"
Nieman Marcus: "v-neck," "v neck," "vneck"
Nieman Marcus handled v-neck and v neck the same, delivering the same number and presentation of results. Vneck, however, autocorrects to "neck."
Abercrombie handled all variations of "v-neck" differently both in number of results and order of results shown.
Staples: "inkject printer," "ink jet printer"
How to remedy
1. Check your site search logs. To understand how your customers describe your products, your best starting point is your own site search logs.
2. Use keyword research tools. They're not just for SEOs and PPC managers. Your merchandisers should be familiar with how to use them to identify additional terms to bake into your search tools.
3. Brainstorm. Use your intuition, consider how products are described in other cultures and countries (e.g. slow cookers vs crock pots, tank tops vs vests). Think outside the (search) box.
This is a big job, so start with your top selling products/categories or your top abandoned search terms. Run usability checks to ensure the search results appear the way you want them to.
Don't leave site search on autopilot / auto pilot / auto-pilot!