On a budget, skip The London Pass (Go City) — the spend outweighs the payoff.
£84+ (1-day) to multi-day
Not a place so much as a bet on your own pace: buy it only if you'll genuinely blitz several paid sights a day. At a relaxed pace, or if your highlights are the free national museums (which it doesn't cover), you'll usually lose money versus paying as you go.