In Return of the Jedi, when trying to sneak into the base on a shuttle, Luke said he senses Darth Vader's presence and said he shouldn't have come lest he jeopardize the mission. Darth Vader also sensed Luke, but let him in anyways. Also, Yoda and Obi-Wan could detect the Force in young Anakin.
So if Jedi and Sith can detect each other, why couldn't they detect Senator Palpatine to begin with? It seems like a giant plot hole.
Palpatine was using Force Stealth to hide his Force presence from the Jedi.
From the linked Wookieepedia page:
Force stealth also referred to as Force Concealment or Buried Presence was a power that was used by highly skilled Force-sensitives to mask their Force alignment (Light or Dark), their ability to use the Force, or even their entire presence from other Force sensitives.
Palpatine was the most powerful and notorious user of this power, having hid his dark nature for over three decades from the Jedi Council, even when in the same room.
Jedi Masters Obi-Wan Kenobi and Yoda both used a form of Force concealment to shield themselves from Palpatine and Vader in their exile.
The excerpted wiki page has since been edited. The following answer is unsubstantiated according to this edit. The edit says the author may have remarked upon it, but I have not been able to confirm.
In the new canon, Palpatine used the fact that the Jedi Temple on Coruscant was built over a Sith shrine to hide his identity. This is detailed in Tarkin. Excerpt from Wookieepedia:
During their brief galactic domination, roughly six-thousand years before the outbreak of the Clone Wars, the Sith constructed a shrine on the planet Coruscant. Following the Sith Order's defeat at the hands of their sworn enemies, the Jedi Order, the Jedi Temple was raised over the shrine's foundations in a symbolic attempt to bury the legacy that the Sith had left behind on the galactic capital. Millennia later, this decision would prove disastrous for the Jedi Order, as Darth Sidious, the reigning Dark Lord of the Sith, was able to make ample use of the wellspring of dark side energy that lay at the shrine's heart; clouding the vision of the Jedi Council, and masking his true motives and identity until it was too late.
Granted the answer given by @Sachin is right, but there is more also. Darth Bane initiated the rule of two for several reasons, but one of the primary reasons was for the simple fact that without an enemy the Jedi became apathetic. So yes, Sidious concealed his presence with the force, but the Jedi also were not looking for the Sith after thousands of years. In fact in episode I it is said the Sith were believed to be extinct.
