Finland captured quite a few of them, though unlike with the I-153 I am not sure if they were used operationally:
They were not. The Finns operated three I-16s. The rest were not restored to airworthiness. They were as follows:
VH-201 -> VH-21: Captured in the Winter War of 30 November 1939-13 March 1940,
this aircraft was apparently a Type 18. However on 30 October 1940 an order was given to restore captured I-16s to their original armament, which was cited as two fuselage MGs (7.62 mm) and two cannons in the wings (20 mm).
This would imply a Type 17 or 24. It's possible this was a Type 18 whose armament the Russians had modified. EDIT: Looks like it was a Type 27.
31 December 1940, State Aircraft Factory (VL) hands a/c over to Air Depot
12 March 1941, Air Depot hands a/c over to Squadron 24, a/c flown from VL in Tampere to Sq. 24 at Vesivehmaa Airfield
1 April 1941, flown back to Tampere
15 April 1941, returned to Air Depot
21 April 1941, loaded aboard steamship
Ariel, shipped by German military officials to Stettin, Germany, destination Die Erprobungstelle der Luftwaffe, Reshlin.
A/c not returned, phases and final fate in Germany unknown.
Known FAF flight time 3 h 25 min, official FAF flight time 6 h 20 min.
IR-101: Shot down during the battles over Suursaari in late March 1942, this
Type 6 or Type 5 aircraft was recovered by the Finns and found to be in airworthy condition.
31 March 1942, flown from Suursaari to Kotka
15 April 1942, flown from Kotka to VL Tampere
23 April 1942, relinquished to Air Depot
29 April 1942, relinquished to VL Kuorevesi
25 July 1942, relinquished to Air Depot 1
31 July 1942, received by Air Depot 1
1 August 1942, relinquished to Sq. 6's 3rd Flight
16 November 1942, relinquished to Sq. 30's 2nd Flight
11 June 1943, relinquished to Air Depot for storing
22 June 1943, received by Air Depot
23 June 1943, relinquished to VL Kuorevesi for repairs
25 June 1943, received by VL
26 June 1943, repairs cancelled by Air Depot Chief Lt. Col. Stenbäck, nonetheless Air Depot made a work order the very same day for inspection and repair of the a/c by VL. Instead of being flown over, the a/c had been disassembled and shipped by rail due to overheating of the engine. The work order had an urgency rating of 3.
2 July 1943, a/c ordered to be stored, repairs halted the same day
17 September 1943, FAF HQ orders a/c to be struck
22 September 1943, relinquished as scrap to Air Depot 2
23 September 1943, a/c recommended to be struck
2 November 1943, a/c struck
Known FAF flight time 6 h 50 min, official FAF flight time 6 h 35 min.
VH-22 -> UT-1: This two-seater
I-16UTI based on the I-16 Type 10 EDIT: I-16 Type 15 UTI-4 was captured near the
Svir in September 1941.
6-7 September 1941, evacuated from Troitsankontu Airfield by Field Air Depot 4
17 October 1941, relinquished to Air Depot
27 October 1941, relinquished to VL Tampere
30 October 1941, received by VL Tampere
31 March 1942, relinquished to Air Depot 1 after repairs
1 April 1942, received by Air Depot 1
10 April 1942, relinquished to Sq. 48
10 August 1942, relinquished to Replacement Sq. 35
11 September 1942, relinquished to Air Force scrap storage in Parola, a/c flew from Vesivehmaa Airfield to Parola at 10:30-11:15 am
16 July 1944, recommended struck due to poor general condition
9 August 1944, struck
15 December 1944, relinquished by Air Depot to Air Combat School
Known FAF flight time 39 h 50 min, official FAF flight time 43 h 25 min.
Source: Atso Haapanen (2008):
Punatähdestä hakaristiin [From the Red Star to the Swastika].
EDIT: Corrected a/c types. See the posts below this one.