Very simple script not responding?

If you are trying to access the player's Character, check if it has a Humanoid.

function addxp(hit) 
    local dude = hit.Parent:WaitForChild("Humanoid").Parent
    dude.xp.Value = 1
    script.Parent:Destroy()
end

script.Parent.Touched:connect(addxp)

or you can use the GetPlayerFromCharacter event.

function addxp(hit) 
    local dude = game.Players:GetPlayerFromCharacter(hit.Parent).Character -- accessing the player through the character
    dude.xp.Value = 1
    script.Parent:Destroy()
end

script.Parent.Touched:connect(addxp)

You're leaving out some needed information. Is "xp" something in the character or in the leaderboards?

Anyway, I'll do both.

In character:

script.Parent.Touched:connect(function(hit)
    local dude = hit.Parent:WaitForChild("Humanoid").Parent --Wait for the humanoid, checking if "hit" is a character
    local xp = dude:WaitForChild("xp")
    xp.Value = 1
end)

In player:

script.Parent.Touched:connect(function(hit)
    local dude = hit.Parent:WaitForChild("Humanoid").Parent
    local player = game.Players:GetPlayerFromCharacter(dude)
    local leaderstats = player:WaitForChild("leaderstats")
    local xp = leaderstats:WaitForChild("xp")
    xp.Value = 1
end)

Hope this helps! :)

There cannot be found thing such as Character. Character can be found from game.Players.Player.Character. You should also add the xp To Leaderboards, check out how to in wiki if you don't now: http://wiki.roblox.com/index.php?title=Leaderboards

function getxp(hit)
    for i,Player in ipairs(game.Players:GetPlayers()) do
        if hit.Parent = Player.Character then
        local Character = hit.Parent
        local Player = game.Players:GetPlayerFromCharacter(Character)
        Character.xp.Value = Character.xp.Value +1 --I made this like this, you can do like you want
        script.Parent:Destroy()
    end
end

script.Parent.Touched:connect(getxp)