1. I have a token copy of Ulamog. The token dies. Do I shuffle?
2. I have a Clone of Ulamog. It dies. Do I shuffle?
3. I control a regular Ulamog. An opponent casts Sudden Spoiling on me. Later that turn, Ulamog dies. Do I shuffle?
I recall there being something weird about "from anywhere" graveyard triggers but I don't recall the specifics.
Ulamog's last ability is not a leaves-the-battlefield ability, even if it triggers when the object with it goes to the graveyard from the battlefield, because its trigger condition says "from anywhere" (C.R. 603.6c). Since it's not a leaves-the-battlefield ability and it's not otherwise an exception mentioned in C.R. 603.10 and subrules, what is relevant for the purposes of Ulamog's last ability is the state of the "objects that exist immediately after" the object in question goes to a graveyard from anywhere (C.R. 603.10). Therefore, if the object that entered the graveyard has Ulamog's last ability, that ability will trigger from the graveyard (C.R. 603.2). For clarity, read "When Ulamog, the Infinite Gyre is put into a graveyard from anywhere..." as "When Ulamog, the Infinite Gyre enters a graveyard from anywhere..."
Therefore:
1. I assume here that you're speaking of a "token that's a copy" of Ulamog. A token that's a copy of Ulamog has entered the graveyard, and it has Ulamog's last ability (which doesn't care whether that object is a card or a token), so that ability will trigger. Note that a token can go to the graveyard or anywhere else like any other permanent (C.R. 111.6; see also C.R. 111.8 and this thread). Note also that if a token that's a copy of another object is created, the token's original values will be that other object's copiable values (C.R. 707.2, 707.3, 613.1; see also C.R. 707.5). This is different from a copy effect discussed in question 2 (compare C.R. 613.1 with 613.1a).
2. Not necessarily.Assuming you mean a permanent that's normally a Clone card but enters the battlefield as a copy of Ulamog, no. Clone's copy effect applies only to the permanent that's a copy of Ulamog due to that effect (see also C.R. 611.2c); it doesn't apply to the object that entered the graveyard as given in your question (with the assumption just given), so that that object will not necessarily have Ulamog's last ability.
3. Sudden Spoiling's effect applies only to Ulamog on the battlefield (C.R. 611.2c), not to the object that entered the graveyard as given in your question, so that the object that enters the graveyard this way will have all its usual abilities. In the case of Ulamog, therefore, its last ability will trigger when it enters the graveyard this way.
EDIT: Edited after comment 4 was posted.
EDIT (Jul. 11): Some rules were renumbered with Core Set 2020. Correctness edit.
EDIT (Aug. 13, 2020): Clarification.
EDIT (Oct. 16, 2021): Delete rule citation. Some rules were renumbered in the meantime.
2. Not necessarily. Clone's copy effect applies only to the permanent that's a copy of Ulamog due to that effect (see also C.R. 611.2c); it doesn't apply to the object that entered the graveyard as given in your question, so that that object will not necessarily have Ulamog's last ability.
Not necessarily? I don't understand. Could you give me an example of a situation in which I a) would and b) would not shuffle when a Clone of an Ulamog dies?
Not necessarily? I don't understand. Could you give me an example of a situation in which I a) would and b) would not shuffle when a Clone of an Ulamog dies?
I was thinking of cases when a permanent that is not normally Ulamog becomes a copy of Ulamog and then dies:
a. If a permanent that's normally an Emrakul, the Aeons Torn card somehow becomes a copy of Ulamog and then dies, then the object that enters the graveyard this way is Emrakul, with Emrakul's last ability which is of the form "When[ever] [this object] is put into a graveyard from anywhere, ...", so that ability will trigger when Emrakul enters the graveyard this way.
b. If a permanent that's normally a Clone card (or a Grizzly Bears card) somehow becomes a copy of Ulamog and then dies, then the object that enters the graveyard this way is Clone (or Grizzly Bears, respectively), without an ability of the form "When[ever] [this object] is put into a graveyard from anywhere, ..." to trigger.
1. I have a token copy of Ulamog. The token dies. Do I shuffle?
2. I have a Clone of Ulamog. It dies. Do I shuffle?
3. I control a regular Ulamog. An opponent casts Sudden Spoiling on me. Later that turn, Ulamog dies. Do I shuffle?
I recall there being something weird about "from anywhere" graveyard triggers but I don't recall the specifics.
Therefore:
1. I assume here that you're speaking of a "token that's a copy" of Ulamog. A token that's a copy of Ulamog has entered the graveyard, and it has Ulamog's last ability (which doesn't care whether that object is a card or a token), so that ability will trigger. Note that a token can go to the graveyard or anywhere else like any other permanent (C.R. 111.6; see also C.R. 111.8 and this thread). Note also that if a token that's a copy of another object is created, the token's original values will be that other object's copiable values (C.R. 707.2, 707.3, 613.1; see also C.R. 707.5). This is different from a copy effect discussed in question 2 (compare C.R. 613.1 with 613.1a).
2.
Not necessarily.Assuming you mean a permanent that's normally a Clone card but enters the battlefield as a copy of Ulamog, no. Clone's copy effect applies only to the permanent that's a copy of Ulamog due to that effect (see also C.R. 611.2c); it doesn't apply to the object that entered the graveyard as given in your question (with the assumption just given), so that that object will not necessarily have Ulamog's last ability.3. Sudden Spoiling's effect applies only to Ulamog on the battlefield (C.R. 611.2c), not to the object that entered the graveyard as given in your question, so that the object that enters the graveyard this way will have all its usual abilities. In the case of Ulamog, therefore, its last ability will trigger when it enters the graveyard this way.
EDIT: Edited after comment 4 was posted.
EDIT (Jul. 11): Some rules were renumbered with Core Set 2020. Correctness edit.
EDIT (Aug. 13, 2020): Clarification.
EDIT (Oct. 16, 2021): Delete rule citation. Some rules were renumbered in the meantime.
Not necessarily? I don't understand. Could you give me an example of a situation in which I a) would and b) would not shuffle when a Clone of an Ulamog dies?
a. If a permanent that's normally an Emrakul, the Aeons Torn card somehow becomes a copy of Ulamog and then dies, then the object that enters the graveyard this way is Emrakul, with Emrakul's last ability which is of the form "When[ever] [this object] is put into a graveyard from anywhere, ...", so that ability will trigger when Emrakul enters the graveyard this way.
b. If a permanent that's normally a Clone card (or a Grizzly Bears card) somehow becomes a copy of Ulamog and then dies, then the object that enters the graveyard this way is Clone (or Grizzly Bears, respectively), without an ability of the form "When[ever] [this object] is put into a graveyard from anywhere, ..." to trigger.
Clarifying comment 2.
EDIT (Jul. 11): Correctness edit.