Are there limits to speeds at certain altitudes?
The following maximum speeds apply in the US (A few aren't based on altitude, but I've included them to be more complete):


91.817: Mach 1 over land (with a few exceptions that are noted in Appendix B to 91.817)
91.117(a): 250 KIAS below 10,000 ft. MSL
91.117(b): 200 KIAS below 2,500 ft. within 4NM of the primary airport for Class C and D airspace (unless within Class B airspace)
91.117(c): 200 KIAS under the shelf of Class B airspace
91.117(c): 200 KIAS in a VFR corridor through Class B airspace
AIM 5-3-8(2): Maximum holding speeds:


At or below 6,000 ft. 200 KIAS
6,001 to 14,000 ft. 230 KIAS
Above 14,000 ft 265 KIAS

Some NOTAMs specify a maximum speed when operating within their limits.
AIM 5-7-2: Maximum speed as assigned by ATC


91.117(d): Any of these speeds may be exceeded if the minimum safe airspeed for the aircraft is higher and you notify ATC. 

91.101 and AIM 5-7-2 NOTE 2 state that none of these apply when more than 12 NM from the coast of the united states.  Because of this, you will often see pilots fly at greater than 250 KIAS when below 10,000 feet and more than 12 NM off-shore.

Aircraft specific limitations must also be complied with.