There was a liftershalte, a special spot for hitchhiking, at the beginning of the A2 near the soccer stadium De Geusselt (Viaductweg x N2/A2) (direction Eindhoven) and the A79 (direction Heerlen). With the upgrade of the N2 to A2 this liftershalte was removed.
Currently it is easy to hitchhike out of Maastricht towards Eindhoven and Heerlen / Aachen at the Viaductweg. The spot is located at the crossing of Viaductweg and Meerssenerweg. East of this crossing there is a fair strip of asphalt in the middle (!) of the road, where you can stand. All passing cars enter either the A2 or the A79 here. Preferably use a sign.
It is also very well possible to use this spot to hitchhike towards the motorway Aachen and then on to Köln and further. Some people recommend to catch a lift to Heerlen and then catch another one to Aachen at the junction of A79 and N281.
If you prefer you can also stand about 300 meter north of the former official hitchhiking spot. You can reach the hard shoulder of the N2 from the tunnel at Severenstraat. Cars drive notably faster there.
An alternative for hitchhiking towards the north (especially directions Eindhoven and further can be found at the N2 opposite the Maastricht-Randwyck trainstation. From the station walk up the stairs, turn left on the bridge so that you cross the N2, at the end walk around the soccer fields. Once you are close to the main road, walk through the vegetation and then a couple of 100s of meters along the road (through the ditch to stay safe and smooth) towards the bridge that connects with the Randwyck station. There is a very wide hard shoulder now (2012) and a maximum speed of 50 kmh (cars passing mostly at 50-80 kmh). Note that this location hitchhiking is officially not allowed because of the freeway status.
South towards Liege
Follow the rail track from the central station out of the town in a southern direction from the backside exit (use the bridge over the rails). At the first rail/road crossing south of the station hike on over the cycling path and later, still by the side of the railway, over Gerardusweg. Follow this way until the end, thus you walk under a bridge and you will arrive at a motorway entrance on the junction named Europaplein; some hundreds of meters further on at the other side of the railway is the railway station Maastricht Randwyck. If you stand at the corner of the road across from the sign pointing at the A2/Luik (Liege) you will get a lift.
Best place towards Hasselt is at or just after the traffic lights at the crossing of Via Regia and Canteleerstraat, the first crossing after the traffic square Via Regia. Use a sign. All the motorway access lanes in Hasselt are suitable for either Brussels or Antwerpen.