<p>If I want to use the validation framework that you can use with ASP.NET MVC, will the JavaScript conflict with other JavaScript frameworks like jQuery or YUI?</p>

There are many MVC frameworks. There are many JavaScript frameworks that have different functionalities. If you want a meaningful answer, you should choose an MVC and a JavaScript framework and ask concerning those two. Please be as detailed as possible in your questions.
As an example, the validation handling on ActiveRecord (used in Ruby on Rails) only performs validations on the server end. You can always add JavaScript validations on top of that, but the server-side validations are what really matters for data integrity.