You can, but potentially only in the GSM (2G) network (then, you would get only GPRS / EDGE data connections, no UMTS (3G) ones).

To make sure you can use a North American smartphone also in Europe, you have to look at what frequency bands are supported by the phone, and what frequency bands are in use by the phone networks in your country. Here's an overview:

Frequency GSM
850
GSM
900
GSM
1800
GSM
1900
UMTS
850
UMTS
900
UMTS
1700
UMTS
1800
UMTS
1900
UMTS
2100
North American networks: T-Mobile USA [source] x x x x     x   x  
North American networks: AT&T USA [source] x x x x x       x  
European networks [source] x x x x   x   x   x
HTC Sensation Z710e [source]
T-Mobile version ("Sensation 4G")
x x x x   x x     x
HTC Sensation Z710a [source]
international version, Bell version, Telstra version
x x x x x       x x
HTC Sensation XE Z715e [source, source, source] x x x x   x x     x
HTC Sensation XE Z715a [source]
Telstra version, Vodafone Australia version
x x x x x       x x
HTC Desire HD                    
HTC Desire                    

Effect for Europeans: you can use all of the HTC Sensation / Sensation XE variants in European networks.

Sometimes, the models for the North American and European market carry different names. For example, the "HTC Sensation 4G" is the name given to the HTC Sensation by T-Mobile for launching it in the U.S.. The hardware is just the Z710e version, and it is supported by CyanogenMod 10 (at least) [example].

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