There are no shops dedicated to selling robots in Ireland, so here is a quick guide of useful place in Ireland and online to pick up robotics parts.
Maplin - The best chance of finding electronic parts in Dublin, they have an electronics section in store where you can buy resistors, capacitor packs, soldering Irons, circuit boards, tools etc. It not massive but it is something. They also have a catalogue with a larger selection of electronics which they might have in the stock room if you ask. They will order things in for you if they don't. They have specials most months were you can get some reasonable bargains.
Peats - They used to be more like maplin, but now they focus on consumer electronics (tv, dvd players ...) They still have a small electronic section, but it can be a little hit and miss.
Parnell Street, Dublin map
Lidl and Aldi - Can be useful for buying cheap tools.
Model shops - Not ideal but they may stock servos and tools useful for buliding robots.
Locations -
ebay.ie - Cheap servos, batteries and all sort of components. Handy but the shipping can sometimes make it expensive for small items.
Digikey - Massive selection of electronic components. Free Shipping on orders over 65 euro.
Farnell - Similar to digikey - Free shipping on orders over 30 Euro?
Radionics - similar to digikey and Farnell
Island models - Online model shop. Range of servos and batteries and chargers
(When the euro is strong bargains can be found)
Active robots - large range of robot stuff but not always cheap.
Robosavvy - Probably the best place to buy humanoid robots on the net
Tinker.it - Small selection but worth a look
Skpang Large selection of embedded electronics boards
Yerobot - Arduino compatible boards with a focus on robotics and nice prices
oomlout - open source electronics products, including Arduino. Email them about shipping to Ireland
Sparkfun - Fantastic shop with all sort of electronic goodies
Robotshop - Massive selection of all things robotic. Shipping costs can be reasonable
NKC electronics - Good selection of arduino/freeduino stuff
Trossen Robotics - wide selection
Robot Store - wide selection
Junun - Nice range of sharp distance sensors
Maximum Robotics - Friendly people to deal with. Sometimes stock nice surplus motors with encoders on the cheap.
TME - Wide range of electronic components
NuElectronics - Well priced shop for Arduino clones and some cool display shields
Pololu - Nice range of all things robotics, distributors of their products worldwide
Eagle - printed circuit board design package, with powerful freeware version
KiCad - open source (GPL) software for the creation of electronic schematic diagrams and printed circuit board artwork.
Fritzing - PCB layout creator with a arduino-like philosophy (in beta)