Before going into your question let me list some autocomplete libraries :
- typeahead.js fast autocomplete library from Twitter
- complete.ly JavaScript library for autocompletion
- Marco Polo jQuery Autocomplete plugin
- bassistance jQuery Autocomplete Plugin
- jQuery UI Autocomplete Widget
- jQuery TextEXT Tag Input and Autocomplete
- YUI Autocomplete
- jQuery TokenInput Autocomplete
- jQuery Manifest Input Autocomplete
- Inputosaurus Text Input with Autocomplete
- Live Search 2.0 with Ajax
- Ajax AutoComplete for jQuery
- glAutoTag lightweight auto-complete and tags plugin for jQuery
- Autocomplete Widget for jQuery Mobile
- Autosuggest jQuery Plugin
- jQuery Cool Auto-Suggest
- dhtmlxCombo JavaScript combobox with autocomplete
- VisualSearch.js enhances search boxes with autocomplete faceted
search queries
- jQuery PHP Ajax Autosuggest
- SearchBox jQuery live search autocomplete
- FCBKcomplete facebook-like dynamic inputs with auto complete
- selectToAutocomplete enhances select tags with autocomplete features
- jQuery Plugin Auto Complete
- jQuery Smart Auto Complete plugin
- Select2 jQuery select tag with autocomplete features
- selectize.js textbox and select box hybrid with autocomplete
- Ajax Search Suggest
- Autocompleter for MooTools with JSON, PHP, and MySQL PDO
- Simple Ajax Live Search
- Search suggestion with PHP and MySQL
But the list may not satisfy every compatibility that you may require,i would rather recommend to have used JQuery Autocomplete , Autocomplete Doc
I've had a look at a few options and am currently using jQuery
autocomplete but this is not working correctly on iPhone/iPad
Stack Overflow posts on issues and solutions for ipad / iphones in jQuery auto-complete :
Autocomplete requires you to click twice in iOS after update to 1.11.0
jquery autocomplete ipad hide keyboard focus
JQuery UI autocomplete on iPad
jQuery UI autocomplete needs double tap on iOS
Stack Overflow and other references on implementation :
Getting jQueryUi Autocomplete to work with jQueryMobile
JQuery Autocomplete working in Chrome but not in android using phonegap
detecting and disabling autocompletion on mobile devices with either complete.ly or typeahead
Detecting a mobile browser
Tap head auto suggestion