Search engines come and search engines go; some become extremely popular and others never do. Today there are really one two globally popular search engines, Google, and Bing, which is built by Microsoft. The most recent noteworthy change in this landscape is Yahoo! which formerly used their own technology but is now based on Bing. Yahoo is still included here as it provides somewhat different features compared to Bing itself. Blekko is the newest major search engine, which uses slashtags as their gimmick, slashtags being handy shortcuts for making more sophisticated searches.
Traditionally a web search engine crawls the web to find web pages, indexes them by keyword, and presents a list of the best pages for your search query (a more detailed description can be found in the Wikipedia article linked to below). Most search engines today do this, but add other things in as well. They integrate other types of content (images, video, news, etc.). They often store some information themselves (or partner with a company that does) so that they can include exactly the content you were looking for before the regular search results are listed. An example of that would be showing the actual weather when searching for the weather in your location.
The search engines listed here as hybrids have their search results page made up of various components, usually combining several other search engines, other types of results (images, news, etc.) with their own results, answers, or other features. For particular details on each one, see their websites.
Wolfram|Alpha doesn’t include an index of web pages or use results from another search engine. Instead they only search their own sets of curated data. Both Wolfram|Alpha and True Knowledge are more like “computing” engines, as they try to understand the actual meaning behind your query/question and calculate an answer for it, but their approach differs considerably. Wolfram|Alpha presents results with rich data and graphics and limited interactivity, while True Knowlege focuses more on being able to give concise factual answers. True Knowledge's information comes from extracting them from web pages and user-contributed facts. Ask.com is a search engine which has put a lot of focus on handling natural-language questions as well.
Question-and-Answer (QnA) websites (other than SnappyFingers) are essentially web forums where anyone can ask questions and answer others’s questions. The QnA Sites listed as just links on this page are not directly searchable.
These tools search content created in the very recent past. All of them use Twitter as their primary source but most also include others as well.