2 Chronicles 5:14 (KJV) 14 So that the priests could not stand to minister by reason of the cloud: for the glory of the LORD had filled the house of God.
Yes, there have been times when God's presence fills you so much that it is near impossible to contain. For me it is most prevalent during worship. It varies by degree and while I can feel something during almost any worship service, the intensity is generally far less today than it was in the 1980s, where I think a move of God was far more heightened. What occurs can vary quite a bit. The greatest is when conviction comes, and the person knows they have sinned and is absolutely repentant. Study your old revivals by Pentecostals, some meetings had people start confessing their sin openly and the entire congregation soon was enveloped in public repentance, crying literally to God. Sometimes this also happens individually, as the Holy Spirit will convict you if you have a conscience turned to Him.
The Holy Spirit moves in all kids of ways, sometimes it has a distinct purpose and might be limited, or it can be more corporate like the scripture above.
The greatest corporate move I ever saw was at a Christian camp for teens. I was in a band and we played two worship songs alternating them for about one hour. The audience was enveloped by the Holy Spirit, teens were falling over drunk, some prophesying over one another, some laying hands on others, many speaking in tongues. Some in the band had to stop at times as the Holy Spirit was so strong. Of course some will say this was not God, but one can discern such things. God was in the camp, lives were touched and I doubt anyone there would ever forget it. I have seen similar moves of God in smaller ways. I have also seen counterfeits, or where people (on a smaller scale) will just do the same things in the flesh.
As to hands feeling like electricity, that happens, and I believe it is the Holy Spirit activating a gift, or just giving a blessing of His Presence. I'm just guessing but many feel the Holy Spirit in some way at nearly every worship service. That is why I raise my hands. (In addition to it being scriptural) I extend them and feel God's presence sometimes just barely, other times quite immensely. (Announcements in the middle of worship just about kill of the Holy Spirit by the way, I doubt he is amused by smoke, fleshly songs, or other such activities that try to hype the service).
Electricity or feelings by the Holy Spirit also occur sometimes with the laying on of hands. One can not order this at will though, the strongest times sometimes occur when you least expect it. I know some feel that you can also get devils this way, but I always figure that if you ask God for bread, you will not get a stone. This though would not apply if you knowingly allows someone to lay hands on you that you knew was not in a relationship with God. Again, some copy this stuff in the flesh, pushing people over in a healing line, or prophesying something with little or no meaning etc.
Heat and burning is most often associated with people who are being healed. I have not really experienced this but from others this seems to occur with healing, though it might also occur more generally with certain people. I think that alot of this is dependent on your giftings and callings.
