server.R

require(shiny)
require(rCharts)

inputChoices <- c("A", "B", "C", "D")

shinyServer(function(input, output, session){
    
  	input2Choices <- reactive({
  		inputChoices[-grep(input$input1, inputChoices)]
  	})

  	output$input1 <- renderUI({
  		selectInput("input1", "Input 1:", choices=as.list(inputChoices))
  	})

  	output$input2 <- renderUI({
  		if(is.null(input$input1))
  			return()
  		selectInput("input2", "Input 2:", choices=input2Choices())
  	})
  	
  	output$show <- renderPrint({
  		if(is.null(input$input1))
  			return()
  		print(carrierInput1())
  	})

	output$show2 <- renderPrint({
		print(carrierInput2())
		Sys.sleep(2)
  	})

  	carrierInput1 <- reactive({
    switch(input$input1,
           "A" = 1,
           "B" = 2,
           "C" = 3,
           "D" = 4)
  })

  	carrierInput2 <- reactive({
    switch(input$input2,
           "A" = 1,
           "B" = 2,
           "C" = 3,
           "D" = 4)
  })


})

ui.R

require(shiny)
require(rCharts)
shinyUI(pageWithSidebar(
  headerPanel("Dynamic UI inputs with Shiny"),
  sidebarPanel(
    uiOutput('input1'),
    uiOutput('input2')
  ),
  mainPanel(
   verbatimTextOutput("show"),
   verbatimTextOutput("show2")
  )
))