Does Haste let a creature use activated abilities that require tapping the turn it enters the battlefield?

Normally, a creature cannot attack or activate abilities that include the tap symbol (or untap symbol) in their cost unless it has been under your control since the beginning of your most recent turn. This restriction is commonly called 'summoning sickness' and is defined in CR 302.6.

Haste (CR 702.10a) specifically overrides this restriction. A creature with Haste can attack and can activate activated abilities that include {T} or {Q} in their cost the very same turn it enters the battlefield under your control.

It is important to note that Haste only removes the CR 302.6 restriction. Other timing rules still apply — for example, you can still only activate a tap ability at a time you could normally activate it (i.e., usually at sorcery speed for sorcery-speed abilities, or at instant speed for others). Haste does not give you permission to do things beyond removing the freshness restriction.

Concrete example: You cast Goblin Welder (which has Haste and an activated ability that includes {T}) on your main phase. Because it has Haste, you can immediately tap it to activate its ability that same turn, even though it just entered the battlefield.

If the creature does not have Haste, you must wait until your next turn (or another turn it remains under your control continuously through the start of your turn) before you can tap it for an activated ability.